Syntomic complexes and p-adic nearby cycles
We compute syntomic cohomology of semistable affinoids in terms of cohomology of ( φ , Γ ) -modules which, thanks to work of Fontaine–Herr, Andreatta–Iovita, and Kedlaya–Liu, is known to compute Galois cohomology of these affinoids. For a semistable scheme over a mixed characteristic local ring this...
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| Veröffentlicht in: | Inventiones mathematicae Jg. 208; H. 1; S. 1 - 108 |
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| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.04.2017
Springer Verlag |
| Schlagworte: | |
| ISSN: | 0020-9910, 1432-1297 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We compute syntomic cohomology of semistable affinoids in terms of cohomology of
(
φ
,
Γ
)
-modules which, thanks to work of Fontaine–Herr, Andreatta–Iovita, and Kedlaya–Liu, is known to compute Galois cohomology of these affinoids. For a semistable scheme over a mixed characteristic local ring this implies a comparison isomorphism, up to some universal constants, between truncated sheaves of
p
-adic nearby cycles and syntomic cohomology sheaves. This generalizes the comparison results of Kato, Kurihara, and Tsuji for small Tate twists (where no constants are necessary) as well as the comparison result of Tsuji that holds over the algebraic closure of the field. As an application, we combine this local comparison isomorphism with the theory of finite dimensional Banach Spaces and finiteness of étale cohomology of rigid analytic spaces proved by Scholze to prove a Semistable conjecture for formal schemes with semistable reduction. |
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| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 0020-9910 1432-1297 |
| DOI: | 10.1007/s00222-016-0683-3 |