Arithmetic statistics for Galois deformation rings
Given an elliptic curve E defined over the rational numbers and a prime p at which E has good reduction, we consider the Galois deformation ring parametrizing lifts of the residual representation on the p -torsion group E [ p ]. The deformations considered are subject to the flat condition at p . Fo...
Uloženo v:
| Vydáno v: | The Ramanujan journal Ročník 64; číslo 3; s. 685 - 708 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.07.2024
|
| Témata: | |
| ISSN: | 1382-4090, 1572-9303 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Given an elliptic curve
E
defined over the rational numbers and a prime
p
at which
E
has good reduction, we consider the Galois deformation ring parametrizing lifts of the residual representation on the
p
-torsion group
E
[
p
]. The deformations considered are subject to the flat condition at
p
. For a fixed elliptic curve without complex multiplication, it is shown that these deformation rings are unobstructed for all but finitely many primes. For a fixed prime
p
and varying elliptic curve
E
, we relate the problem to the question of how often
p
does not divide the modular degree. Heuristics due to M.Watkins based on those of Cohen and Lenstra indicate that this proportion should be
∏
i
≥
1
1
-
1
p
i
≈
1
-
1
p
-
1
p
2
. This heuristic is supported by computations which indicate that most elliptic curves (satisfying further conditions) have smooth deformation rings at a given prime
p
≥
5
, and this proportion comes close to
100
%
as
p
gets larger. |
|---|---|
| AbstractList | Given an elliptic curve
E
defined over the rational numbers and a prime
p
at which
E
has good reduction, we consider the Galois deformation ring parametrizing lifts of the residual representation on the
p
-torsion group
E
[
p
]. The deformations considered are subject to the flat condition at
p
. For a fixed elliptic curve without complex multiplication, it is shown that these deformation rings are unobstructed for all but finitely many primes. For a fixed prime
p
and varying elliptic curve
E
, we relate the problem to the question of how often
p
does not divide the modular degree. Heuristics due to M.Watkins based on those of Cohen and Lenstra indicate that this proportion should be
∏
i
≥
1
1
-
1
p
i
≈
1
-
1
p
-
1
p
2
. This heuristic is supported by computations which indicate that most elliptic curves (satisfying further conditions) have smooth deformation rings at a given prime
p
≥
5
, and this proportion comes close to
100
%
as
p
gets larger. |
| Author | Weston, Tom Ray, Anwesh |
| Author_xml | – sequence: 1 givenname: Anwesh surname: Ray fullname: Ray, Anwesh email: anwesh@cmi.ac.in organization: Chennai Mathematical Institute, H1, SIPCOT IT Park – sequence: 2 givenname: Tom surname: Weston fullname: Weston, Tom organization: Department of Mathematics, University of Massachusetts |
| BookMark | eNp9j8tOwzAQRS1UJNrCD7DKDxjGD2J7WVVQkCqxgbVl_ABXTVJ5woK_xyGsu5o7Gp3RPSuy6Ic-EnLL4I4BqHtkjAlDgUsKoKd0QZbsQXFqBIhFzUJzKsHAFVkhHgBAglBLwjclj19dHLNvcHRjxpqwSUNpdu44ZGxCrEtXL0PflNx_4jW5TO6I8eZ_rsn70-Pb9pnuX3cv282eei75SFloWwFMRyeCielDGgdSK6Yhae40l8Ep6bUXgcu2ldEor7hIwgRwDCq1Jnz-68uAWGKyp5I7V34sAztZ29naVmv7Z22hQmKG8DSVjcUehu_S157nqF-1xFu5 |
| Cites_doi | 10.24033/asens.1437 10.5802/jtnb.936 10.1080/10586458.2002.10504701 10.1090/S0894-0347-09-00628-6 10.1016/j.jnt.2004.01.010 10.1090/S0273-0979-1990-15937-3 10.1007/BF01239511 10.1007/s11856-009-0017-x 10.2307/2118560 10.1007/978-1-4613-9649-9_7 10.2307/3597186 10.1016/j.ansens.2004.09.001 10.4007/annals.2014.179.2.3 10.1007/978-1-4614-1260-1_2 10.1353/ajm.2004.0052 10.1007/s10240-008-0015-2 10.1017/S1474748002000038 10.1007/BF01405086 10.1142/S1793042116500160 10.2307/2118559 10.1007/s10240-008-0016-1 10.2140/ant.2020.14.1331 10.1007/978-1-4612-3460-9_3 10.2977/prims/31 10.1090/S0894-0347-01-00370-8 |
| ContentType | Journal Article |
| Copyright | The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s11139-024-00839-0 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1572-9303 |
| EndPage | 708 |
| ExternalDocumentID | 10_1007_s11139_024_00839_0 |
| GrantInformation_xml | – fundername: Simons Foundation funderid: http://dx.doi.org/10.13039/100000893 |
| GroupedDBID | -5D -5G -BR -EM -Y2 -~C .86 .VR 06D 0R~ 0VY 123 1N0 1SB 203 29P 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5VS 67Z 6NX 6TJ 8TC 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADQRH ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGWIL AGWZB AGYKE AHAVH AHBYD AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z J9A JBSCW JCJTX JZLTJ KDC KOV LAK LLZTM M4Y MA- N2Q NB0 NPVJJ NQJWS NU0 O9- O93 O9J OAM OVD P9R PF0 PT4 PT5 QOS R89 R9I RIG RNI ROL RPX RSV RZC RZE RZK S16 S1Z S27 S3B SAP SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TEORI TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z7U ZMTXR ~A9 AAPKM AAYXX ABBRH ABDBE ABFSG ABJCF ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFKRA AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA AZQEC BENPR BGLVJ CCPQU CITATION DWQXO GNUQQ HCIFZ M2P M7S PHGZM PHGZT PQGLB PTHSS |
| ID | FETCH-LOGICAL-c242t-1d663018ea3d9efb49a0487180f82a824da74c8c3d24664e97c723f39d0a10ea3 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001226922200001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1382-4090 |
| IngestDate | Sat Nov 29 03:21:00 EST 2025 Fri Feb 21 02:41:39 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | Galois deformation rings 11G05 Distribution questions 11F80 11R45 Galois deformations Unobstructedness |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c242t-1d663018ea3d9efb49a0487180f82a824da74c8c3d24664e97c723f39d0a10ea3 |
| PageCount | 24 |
| ParticipantIDs | crossref_primary_10_1007_s11139_024_00839_0 springer_journals_10_1007_s11139_024_00839_0 |
| PublicationCentury | 2000 |
| PublicationDate | 20240700 2024-07-00 |
| PublicationDateYYYYMMDD | 2024-07-01 |
| PublicationDate_xml | – month: 7 year: 2024 text: 20240700 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationSubtitle | An International Journal Devoted to the Areas of Mathematics Influenced by Ramanujan |
| PublicationTitle | The Ramanujan journal |
| PublicationTitleAbbrev | Ramanujan J |
| PublicationYear | 2024 |
| Publisher | Springer US |
| Publisher_xml | – name: Springer US |
| References | DiamondFFlachMGuoLThe Tamagawa number conjecture of adjoint motives of modular formsAnn. Sci. l’Ecole Normale Supérieure2004375663727210347110.1016/j.ansens.2004.09.001 TaylorRichardAutomorphy for some l-adic lifts of automorphic mod l Galois representations. IIPubl. Math.20081081183239247068810.1007/s10240-008-0015-2 DukeWilliamElliptic curves with no exceptional primesC. R. Acad. Sci. Série 1 Math.1997325.88138181485897 RamakrishnaRaviOn a variation of Mazur’s deformation functorCompos. Math.19938732692861227448 WilesAndrewModular elliptic curves and Fermat’s last theoremAnn. Math.19951413443551133303510.2307/2118559 NeukirchJSchmidtAWingbergKCohomology of Number Fields2013New YorkSpringer WestonTomUnobstructed modular deformation problemsAm. J. Math.2004126612371252210239410.1353/ajm.2004.0052 Cremona, J. E., Sadek, M.: Local and global densities for Weierstrass models of elliptic curves. arXiv preprint arXiv:2003.08454 (2020) RamakrishnaRDeforming Galois representations and the conjectures of Serre and Fontaine-MazurAnn. Math.2002156115154193584310.2307/3597186 Boston, N., Mazur, B.: Explicit universal deformations of Galois representations. Mathematical Society of Japan, Algebraic Number Theory-in honor of K. Iwasawa (1989) SerreJean-PierreGalois Properties of Finite Order Points of Elliptic CurvesInvent. Math.19721525933138728310.1007/BF01405086 TaylorRichardWilesARing-theoretic properties of certain Hecke algebrasAnn. Math.1995141553572133303610.2307/2118560 GuiraudDavid-AlexandreUnobstructedness of Galois deformation rings associated to regular algebraic conjugate self-dual cuspidal automorphic representationsAlgebra Number Theory202014613311380414905410.2140/ant.2020.14.1331 Barnet-LambTGeraghtyDHarrisMTaylorRA family of Calabi-Yau varieties and potential automorphy IIPubl. Res. Inst. Math. Sci.20114712998282772310.2977/prims/31 HatleyJeffreyObstruction criteria for modular deformation problemsInt. J. Number Theory20161201273285345527910.1142/S1793042116500160 KisinMarkThe Fontaine-Mazur conjecture for GL2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{GL}}_2$$\end{document}J. Am. Math. Soc.200922364169010.1090/S0894-0347-09-00628-6 Boston, N.: Deformations of Galois Representations Associated to the Cusp Form Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta $$\end{document}. Séminaire de Théorie des Nombres, Paris 1987-88, pp. 51-62. Birkhäuser, Boston, MA (1990) Mazur, B.: Deforming galois representations. Galois Groups over Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Q}}$$\end{document}, PP 385–437. Springer, New York (1989) BreuilCOn the modularity of elliptic curves over Q: wild 3-adic exercisesJ. Am. Math. Soc.2001144843939183991810.1090/S0894-0347-01-00370-8 ClozelLaurentHarrisMichaelTaylorRichardAutomorphy for some l-adic lifts of automorphic mod l Galois representationsPubl. Math. l’IHÉS20081081181247068710.1007/s10240-008-0016-1 TaylorRichardRemarks on a conjecture of Fontaine and MazurJ. Inst. Math. Jussieu200211125143195494110.1017/S1474748002000038 MazurBarryAn Introduction to the Deformation Theory of Galois Representations1997New YorkSpringer243311 CalegariFrankEmertonMatthewElliptic curves of odd modular degreeIsrael J. Math.20091691417444246091210.1007/s11856-009-0017-x GamzonAdamUnobstructed Hilbert modular deformation problemsJ. Théorie Nombres Bordeaux2016281221236346461910.5802/jtnb.936 BrumerAMcGuinnessOThe behavior of the Mordell-Weil group of elliptic curvesBull. Am. Math. Soc.1990232375382104417010.1090/S0273-0979-1990-15937-3 WestonTomExplicit unobstructed primes for modular deformation problems of squarefree levelJ. Number Theory20051101199218211468110.1016/j.jnt.2004.01.010 Agashe, A., Ribet, K.A., Stein, W.A.: The modular degree, congruence primes, and multiplicity one. In: Number Theory, Analysis and Geometry, pp 19-49. Springer, Boston (2012) Ridgdill, P.: On the Frequency of Finitely Anomalous Elliptic Curves (unpublished dissertation). University of Massachusetts, Amherst (2010) WatkinsMarkComputing the modular degree of an elliptic curveExp. Math.2002114487502196964110.1080/10586458.2002.10504701 FontaineJean-MarcLaffailleGConstruction de représentations p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ p $$\end{document}-adiquesAnn. Sci. l’École Normale Supérieure198215454760870732810.24033/asens.1437 MazurBarryAn infinite fern in the universal deformation space of Galois representationsCollectanea Math.19974821551931464022 Barnet-LambTGeeTGeraghtyDTaylorRPotential automorphy and change of weightAnn. Math.2014179501609315294110.4007/annals.2014.179.2.3 BöckleGPresentations of universal deformation ringsLond. Math. Soc. Notes Ser.2005567572 BostonNigelExplicit deformation of Galois representationsInvent. Math.19911031181196107984210.1007/BF01239511 Brinon, O., Conrad, B.: CMI summer school notes on p-adic Hodge theory (2009) Richard Taylor (839_CR29) 1995; 141 Tom Weston (839_CR34) 2004; 126 Ravi Ramakrishna (839_CR25) 1993; 87 Richard Taylor (839_CR32) 2002; 1 Frank Calegari (839_CR11) 2009; 169 839_CR27 Adam Gamzon (839_CR16) 2016; 28 Jeffrey Hatley (839_CR19) 2016; 12 Nigel Boston (839_CR7) 1991; 103 839_CR21 F Diamond (839_CR14) 2004; 37 Andrew Wiles (839_CR33) 1995; 141 T Barnet-Lamb (839_CR3) 2014; 179 Richard Taylor (839_CR30) 2008; 108 William Duke (839_CR15) 1997; 325.8 J Neukirch (839_CR24) 2013 G Böckle (839_CR5) 2005; 567 A Brumer (839_CR10) 1990; 23 839_CR13 David-Alexandre Guiraud (839_CR17) 2020; 14 R Ramakrishna (839_CR26) 2002; 156 T Barnet-Lamb (839_CR2) 2011; 47 Barry Mazur (839_CR23) 1997; 48 839_CR1 Mark Kisin (839_CR20) 2009; 22 Mark Watkins (839_CR31) 2002; 11 Tom Weston (839_CR35) 2005; 110 839_CR6 Jean-Marc Fontaine (839_CR18) 1982; 15 Laurent Clozel (839_CR12) 2008; 108 839_CR9 839_CR8 Barry Mazur (839_CR22) 1997 Jean-Pierre Serre (839_CR28) 1972; 15 C Breuil (839_CR4) 2001; 14 |
| References_xml | – reference: Cremona, J. E., Sadek, M.: Local and global densities for Weierstrass models of elliptic curves. arXiv preprint arXiv:2003.08454 (2020) – reference: Boston, N.: Deformations of Galois Representations Associated to the Cusp Form Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta $$\end{document}. Séminaire de Théorie des Nombres, Paris 1987-88, pp. 51-62. Birkhäuser, Boston, MA (1990) – reference: RamakrishnaRaviOn a variation of Mazur’s deformation functorCompos. Math.19938732692861227448 – reference: BreuilCOn the modularity of elliptic curves over Q: wild 3-adic exercisesJ. Am. Math. Soc.2001144843939183991810.1090/S0894-0347-01-00370-8 – reference: MazurBarryAn infinite fern in the universal deformation space of Galois representationsCollectanea Math.19974821551931464022 – reference: WatkinsMarkComputing the modular degree of an elliptic curveExp. Math.2002114487502196964110.1080/10586458.2002.10504701 – reference: Agashe, A., Ribet, K.A., Stein, W.A.: The modular degree, congruence primes, and multiplicity one. In: Number Theory, Analysis and Geometry, pp 19-49. Springer, Boston (2012) – reference: Barnet-LambTGeraghtyDHarrisMTaylorRA family of Calabi-Yau varieties and potential automorphy IIPubl. Res. Inst. Math. Sci.20114712998282772310.2977/prims/31 – reference: WestonTomExplicit unobstructed primes for modular deformation problems of squarefree levelJ. Number Theory20051101199218211468110.1016/j.jnt.2004.01.010 – reference: BostonNigelExplicit deformation of Galois representationsInvent. Math.19911031181196107984210.1007/BF01239511 – reference: DiamondFFlachMGuoLThe Tamagawa number conjecture of adjoint motives of modular formsAnn. Sci. l’Ecole Normale Supérieure2004375663727210347110.1016/j.ansens.2004.09.001 – reference: FontaineJean-MarcLaffailleGConstruction de représentations p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ p $$\end{document}-adiquesAnn. Sci. l’École Normale Supérieure198215454760870732810.24033/asens.1437 – reference: TaylorRichardRemarks on a conjecture of Fontaine and MazurJ. Inst. Math. Jussieu200211125143195494110.1017/S1474748002000038 – reference: MazurBarryAn Introduction to the Deformation Theory of Galois Representations1997New YorkSpringer243311 – reference: RamakrishnaRDeforming Galois representations and the conjectures of Serre and Fontaine-MazurAnn. Math.2002156115154193584310.2307/3597186 – reference: SerreJean-PierreGalois Properties of Finite Order Points of Elliptic CurvesInvent. Math.19721525933138728310.1007/BF01405086 – reference: WilesAndrewModular elliptic curves and Fermat’s last theoremAnn. Math.19951413443551133303510.2307/2118559 – reference: CalegariFrankEmertonMatthewElliptic curves of odd modular degreeIsrael J. Math.20091691417444246091210.1007/s11856-009-0017-x – reference: KisinMarkThe Fontaine-Mazur conjecture for GL2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{GL}}_2$$\end{document}J. Am. Math. Soc.200922364169010.1090/S0894-0347-09-00628-6 – reference: TaylorRichardWilesARing-theoretic properties of certain Hecke algebrasAnn. Math.1995141553572133303610.2307/2118560 – reference: DukeWilliamElliptic curves with no exceptional primesC. R. Acad. Sci. Série 1 Math.1997325.88138181485897 – reference: BrumerAMcGuinnessOThe behavior of the Mordell-Weil group of elliptic curvesBull. Am. Math. Soc.1990232375382104417010.1090/S0273-0979-1990-15937-3 – reference: BöckleGPresentations of universal deformation ringsLond. Math. Soc. Notes Ser.2005567572 – reference: Mazur, B.: Deforming galois representations. Galois Groups over Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Q}}$$\end{document}, PP 385–437. Springer, New York (1989) – reference: HatleyJeffreyObstruction criteria for modular deformation problemsInt. J. Number Theory20161201273285345527910.1142/S1793042116500160 – reference: TaylorRichardAutomorphy for some l-adic lifts of automorphic mod l Galois representations. IIPubl. Math.20081081183239247068810.1007/s10240-008-0015-2 – reference: WestonTomUnobstructed modular deformation problemsAm. J. Math.2004126612371252210239410.1353/ajm.2004.0052 – reference: NeukirchJSchmidtAWingbergKCohomology of Number Fields2013New YorkSpringer – reference: Ridgdill, P.: On the Frequency of Finitely Anomalous Elliptic Curves (unpublished dissertation). University of Massachusetts, Amherst (2010) – reference: Brinon, O., Conrad, B.: CMI summer school notes on p-adic Hodge theory (2009) – reference: Boston, N., Mazur, B.: Explicit universal deformations of Galois representations. Mathematical Society of Japan, Algebraic Number Theory-in honor of K. Iwasawa (1989) – reference: GuiraudDavid-AlexandreUnobstructedness of Galois deformation rings associated to regular algebraic conjugate self-dual cuspidal automorphic representationsAlgebra Number Theory202014613311380414905410.2140/ant.2020.14.1331 – reference: Barnet-LambTGeeTGeraghtyDTaylorRPotential automorphy and change of weightAnn. Math.2014179501609315294110.4007/annals.2014.179.2.3 – reference: ClozelLaurentHarrisMichaelTaylorRichardAutomorphy for some l-adic lifts of automorphic mod l Galois representationsPubl. Math. l’IHÉS20081081181247068710.1007/s10240-008-0016-1 – reference: GamzonAdamUnobstructed Hilbert modular deformation problemsJ. Théorie Nombres Bordeaux2016281221236346461910.5802/jtnb.936 – volume: 15 start-page: 547 issue: 4 year: 1982 ident: 839_CR18 publication-title: Ann. Sci. l’École Normale Supérieure doi: 10.24033/asens.1437 – volume: 48 start-page: 155 issue: 2 year: 1997 ident: 839_CR23 publication-title: Collectanea Math. – volume: 28 start-page: 221 issue: 1 year: 2016 ident: 839_CR16 publication-title: J. Théorie Nombres Bordeaux doi: 10.5802/jtnb.936 – volume: 11 start-page: 487 issue: 4 year: 2002 ident: 839_CR31 publication-title: Exp. Math. doi: 10.1080/10586458.2002.10504701 – volume: 22 start-page: 641 issue: 3 year: 2009 ident: 839_CR20 publication-title: J. Am. Math. Soc. doi: 10.1090/S0894-0347-09-00628-6 – ident: 839_CR27 – ident: 839_CR9 – start-page: 243 volume-title: An Introduction to the Deformation Theory of Galois Representations year: 1997 ident: 839_CR22 – volume: 110 start-page: 199 issue: 1 year: 2005 ident: 839_CR35 publication-title: J. Number Theory doi: 10.1016/j.jnt.2004.01.010 – volume: 23 start-page: 375 issue: 2 year: 1990 ident: 839_CR10 publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0273-0979-1990-15937-3 – volume: 103 start-page: 181 issue: 1 year: 1991 ident: 839_CR7 publication-title: Invent. Math. doi: 10.1007/BF01239511 – volume: 169 start-page: 417 issue: 1 year: 2009 ident: 839_CR11 publication-title: Israel J. Math. doi: 10.1007/s11856-009-0017-x – volume: 141 start-page: 553 year: 1995 ident: 839_CR29 publication-title: Ann. Math. doi: 10.2307/2118560 – ident: 839_CR21 doi: 10.1007/978-1-4613-9649-9_7 – volume: 156 start-page: 115 year: 2002 ident: 839_CR26 publication-title: Ann. Math. doi: 10.2307/3597186 – volume: 567 start-page: 572 year: 2005 ident: 839_CR5 publication-title: Lond. Math. Soc. Notes Ser. – volume: 37 start-page: 663 issue: 5 year: 2004 ident: 839_CR14 publication-title: Ann. Sci. l’Ecole Normale Supérieure doi: 10.1016/j.ansens.2004.09.001 – volume: 179 start-page: 501 year: 2014 ident: 839_CR3 publication-title: Ann. Math. doi: 10.4007/annals.2014.179.2.3 – ident: 839_CR1 doi: 10.1007/978-1-4614-1260-1_2 – volume: 325.8 start-page: 813 year: 1997 ident: 839_CR15 publication-title: C. R. Acad. Sci. Série 1 Math. – volume: 126 start-page: 1237 issue: 6 year: 2004 ident: 839_CR34 publication-title: Am. J. Math. doi: 10.1353/ajm.2004.0052 – ident: 839_CR13 – volume: 108 start-page: 183 issue: 1 year: 2008 ident: 839_CR30 publication-title: Publ. Math. doi: 10.1007/s10240-008-0015-2 – volume: 1 start-page: 125 issue: 1 year: 2002 ident: 839_CR32 publication-title: J. Inst. Math. Jussieu doi: 10.1017/S1474748002000038 – ident: 839_CR8 – volume-title: Cohomology of Number Fields year: 2013 ident: 839_CR24 – volume: 15 start-page: 259 year: 1972 ident: 839_CR28 publication-title: Invent. Math. doi: 10.1007/BF01405086 – volume: 12 start-page: 273 issue: 01 year: 2016 ident: 839_CR19 publication-title: Int. J. Number Theory doi: 10.1142/S1793042116500160 – volume: 141 start-page: 443 issue: 3 year: 1995 ident: 839_CR33 publication-title: Ann. Math. doi: 10.2307/2118559 – volume: 108 start-page: 1 year: 2008 ident: 839_CR12 publication-title: Publ. Math. l’IHÉS doi: 10.1007/s10240-008-0016-1 – volume: 14 start-page: 1331 issue: 6 year: 2020 ident: 839_CR17 publication-title: Algebra Number Theory doi: 10.2140/ant.2020.14.1331 – ident: 839_CR6 doi: 10.1007/978-1-4612-3460-9_3 – volume: 87 start-page: 269 issue: 3 year: 1993 ident: 839_CR25 publication-title: Compos. Math. – volume: 47 start-page: 29 issue: 1 year: 2011 ident: 839_CR2 publication-title: Publ. Res. Inst. Math. Sci. doi: 10.2977/prims/31 – volume: 14 start-page: 843 issue: 4 year: 2001 ident: 839_CR4 publication-title: J. Am. Math. Soc. doi: 10.1090/S0894-0347-01-00370-8 |
| SSID | ssj0004037 |
| Score | 2.3193855 |
| Snippet | Given an elliptic curve
E
defined over the rational numbers and a prime
p
at which
E
has good reduction, we consider the Galois deformation ring parametrizing... |
| SourceID | crossref springer |
| SourceType | Index Database Publisher |
| StartPage | 685 |
| SubjectTerms | Combinatorics Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Mathematics Mathematics and Statistics Number Theory |
| Title | Arithmetic statistics for Galois deformation rings |
| URI | https://link.springer.com/article/10.1007/s11139-024-00839-0 |
| Volume | 64 |
| WOSCitedRecordID | wos001226922200001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1572-9303 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0004037 issn: 1382-4090 databaseCode: RSV dateStart: 19970301 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3PS8MwGP3Q6UEP_hbnL3LwpoE06WxyHOL0oEP8xW4lbb7iYG6yTv9-v2TtxkAEvfWQJuGRr--F5L0CnLksjwUqxxNrCx5bJbgRynLv2aTdWEuhDSGud0m3q3s981CZwsr6tnt9JBm-1HOzW0RqhROncK8b6GkZVojutC_Hx6fXuRtShKRMH65HuyMjKqvMz30s0tHiWWigmM7m_ya3BRuVpGTt6RrYhiUc7sD6_SyPtdwF2R73J2_v3rDIvIVoms7MSLCyGzsY9UvmcGZjZH7kcg9eOtfPV7e8-lsCz4lmJzxyJB5EpNEqZ7DIYmOpOol6RKGl1TJ2NolznSsnfaQ8miRPpCqUccJGgt7ah8ZwNMQDYEmGWW40RoUUMXWbkUxC4y4RWxhb0WrCeQ1a-jENxUjn8cceiZSQSAMSqWjCRY1ZWhVI-Uvzw781P4I1GWD3N2iPoTEZf-IJrOZfBOX4NKyMb33FsZ0 |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1dS8MwFL3oFNQHv8X52QffNJA2mW0ehzgnbkN0yt5C2tyygW6yTn-_N127MRBB3_qQpuUk6Tkh95wCXNg4kRyFZaExKZNGcKa4MMx5Nmk3VhNo8hDXVtjpRL2eeixMYVlZ7V4eSeZf6rnZzSe1wohTmNMNdLUMK5IYyxXyPT2_zt2QPE_KdOF6tDtSvLDK_NzHIh0tnoXmFNPY-t_LbcNmISm9-nQO7MASDndhoz3LY832IKiPB5P-uzMses5CNE1n9kiwenfmbTTIPIszG6Pnnpztw0vjtnvTZMXfElhCNDthviXxwP0IjbAK01gqQ6uTqIenUWCiQFoTyiRKhA1cpDyqMAkDkQplufE53XUAleFoiIfghTHGiYrQTwMuqduYZBIqe41YQ2l4rQqXJWj6YxqKoefxxw4JTUjoHAnNq3BVYqaLBZL90vzob83PYa3Zbbd0677zcAzrQT4Erpr2BCqT8SeewmryRbCOz_JZ8g3csrSB |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1dS8MwFL3oFNEHv8X52QffNJg2mW0ehzoV5xj4wd5K2tziQLuxVn-_N223ORBBfOtDGsJJwjmX5JwAnJgolhyFYb7WCZNacKa40Mx6NqkaawjURYhr2-90gl5Pdb-5-Ivb7uMjydLTYFOa0vx8aJLzqfHNJeXCiF-Y1RD0NQ8L0j4aZOv1x5epM5IXqZk2aI8qJcUr28zPfcxS0-y5aEE3rbX_D3QdViup6TTLtbEBc5huwsrDJKc12wKvOernr-_WyOhYa1GZ2uyQkHVu9NugnzkGJ_ZGx44i24bn1vXT5S2rXlFgMdFvzlxDooK7AWphFCaRVJp2LVESTwJPB5402pdxEAvj2ah5VH7seyIRynDtcvprB2rpIMVdcPwIo1gF6CYel9RtRPIJlblAbKDUvFGH0zGA4bAMywinscgWiZCQCAskQl6HszF-YbVxsl-a7_2t-TEsda9aYfuuc78Py14xA_aS7QHU8tEHHsJi_Emojo6KBfMFzjW9ZQ |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Arithmetic+statistics+for+Galois+deformation+rings&rft.jtitle=The+Ramanujan+journal&rft.au=Ray%2C+Anwesh&rft.au=Weston%2C+Tom&rft.date=2024-07-01&rft.pub=Springer+US&rft.issn=1382-4090&rft.eissn=1572-9303&rft.volume=64&rft.issue=3&rft.spage=685&rft.epage=708&rft_id=info:doi/10.1007%2Fs11139-024-00839-0&rft.externalDocID=10_1007_s11139_024_00839_0 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1382-4090&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1382-4090&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1382-4090&client=summon |