Arithmetic, Geometry, Cryptography and Coding Theory
This volume contains the proceedings of the 17th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory (AGC2T-17), held from June 10-14, 2019, at the Centre International de Rencontres Mathématiques in Marseille, France. The conference was dedicated to the memory of Gilles...
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| Médium: | E-kniha |
| Jazyk: | angličtina |
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American Mathematical Society
2021
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| Vydání: | 1 |
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| ISBN: | 9781470454265, 1470454262 |
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- Appendice A. Corrigendum à "Minorations des hauteurs normalisées des sous-variétés de variétés abéliennes II" par Sinnou David et Patrice Philippon -- \frenchrefname -- The quadratic hull of a code and the geometric view on multiplication algorithms -- 1. Introduction -- 2. Multiplication reductions -- 3. An example in dimension 2 -- 4. The canonical point -- 5. The quadratic hull -- 6. Application to geometric realizations -- 7. Experimental results -- 8. Further properties of the quadratic hull -- Acknowledgments -- References -- Serre's genus fifty example -- 1. Introduction -- 2. The elliptic curve -- 3. Constructing the curve via Artin-Schreier extensions -- 4. More equations and intermediate curves -- Acknowledgment -- References -- Back Cover
- Cover -- Title page -- Contents -- Preface -- A new upper bound for the largest complete \boldmath( , )-arc in \boldmath\PG(2, ) -- 1. Introduction -- 2. Some basic equations -- 3. Non-existence of some \boldmath( , )-arcs in \boldmath\PG(2, ) -- 4. New largest bound -- 5. Application of Theorem 4.1 -- Acknowledgment -- References -- Bounds on the minimum distance of algebraic geometry codes defined over some families of surfaces -- 1. Introduction -- 2. Background -- 3. The minimum distance of codes over some families of algebraic surfaces -- 4. Four improvements -- 5. An example: surfaces in \boldmathℙ³ -- Acknowledgments. -- References -- On the number of effective divisors in algebraic function fields defined over a finite field -- 1. Introduction -- 2. Contents -- 3. Non-asymptotical case -- 4. Asymptotical case -- Appendix A. -- References -- The absolute discriminant of the endomorphism ring of most reductions of a non-CM elliptic curve is close to maximal -- 1. Introduction -- 2. Proof of the main theorem -- Acknowledgments -- References -- Toward good families of codes from towers of surfaces -- Introduction -- 1. Codes from surfaces -- 2. Infinite étale towers of surfaces -- 3. Open problems -- Acknowledgments -- References -- Appendix A. On the étale site of marked schemes, \normalfont by Alexander Schmidt -- Acknowledgment -- References -- Sato-Tate groups of abelian threefolds: a preview of the classification -- 1. Introduction -- 2. Background on Sato-Tate groups -- 3. Classification: an overview -- 4. Realization -- References -- Arithmetic, Geometry, and Coding Theory: Homage to Gilles Lachaud -- 1. Gilles Lachaud's early works -- 2. Gilles Lachaud: friend and mathematician -- 3. A Tribute to Gilles Lachaud -- 4. Gilles Lachaud's work -- References -- Elliptic curves with large Tate-Shafarevich groups over \boldmath _{ }( )
- Introduction -- 1. Invariants of elliptic curves over function fields -- 2. The elliptic curves \boldmath _{ , } -- 3. Preliminaries on character sums -- 4. The \boldmath -function of \boldmath _{ , } -- 5. Non-vanishing of \boldmath ( _{ , }, ) at the central point and consequences -- 6. Distribution of the Kloosterman sums \Kloosnᵧ( ) -- 7. Estimates of the central value ( _{ , }, ⁻¹) -- 8. Proof of Theorem C -- Acknowledgments -- References -- On Sato-Tate distributions, extremal traces, and real multiplication in genus 2 -- 1. Introduction -- 2. Background and notation -- 3. Weyl integration formula -- 4. Taylor expansions for the trace function -- 5. On results of Lachaud -- 6. Distribution of extremal traces in families -- 7. Conclusion -- Acknowledgments -- References -- La trace et le deltoïde de \boldmath\SU(3) -- 1. Introduction -- 2. Le groupe unitaire -- 3. Le deltoïde -- 4. Loi du caractère standard -- 5. Loi de la longueur de la trace -- 6. Loi de la norme de la trace -- 7. Loi du caractère de la représentation adjointe -- 8. Loi de la partie réelle du caractère standard -- 9. Loi de la partie imaginaire du caractère standard -- \frenchrefname -- Stable models of plane quartics with hyperelliptic reduction -- 1. Introduction and main result -- 2. Link with theta constants -- 3. A Riemann model providing a good \PHM -- 4. Bitangents of a smooth plane quartic -- 5. The algorithm and an example -- Acknowledgment -- References -- Courbes de genre \boldmath3 avec \boldmath ₃ comme groupe d'automorphismes -- 1. Introduction -- 2. Caractéristique différente de 2 et 3 -- 3. Le cas de caractéristique 3 -- \frenchrefname -- Bornes sur le nombre de points rationnels des courbes : en quête d'uniformité -- 1. Introduction -- 2. Comptage euclidien -- 3. Variante de Lang-Silverman