padic cohomology

General Introduction
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Search results
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Online References
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Paper References
The three Asterisque volumes, see AMS for titles
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
[arXiv:1212.3813] Comparison Isomorphisms for Smooth Formal Schemes from arXiv Front: math.NT by Fabrizio Andreatta, Adrian Iovita For a smooth proper scheme or formal scheme over an unramified, complete DVR of mixed characteristics we prove a comparison isomorphism relating etale cohomology of the generic fiber with values in a crystalline etale sheaf to the crystalline cohomology of its special fiber with values in the associated Fisocrystal.
arXiv:1009.3108 Sur le topos infinitésimal padique d'un schéma lisse I from arXiv Front: math.AG by Alberto Dario Arabia, Zoghman Mebkhout In order to have cohomological operations for de Rham padic cohomology with coefficients as manageable as possible, the main purpose of this paper is to solve intrinsically and from a cohomological point of view the lifting problem of smooth schemes and their morphisms from characteristic p > 0 to characteristic zero which has been one of the fundamental difficulties in the theory of de Rham cohomology of algebraic schemes in positive characteristic since the beginning. We show that although smooth schemes and morphisms fail to lift geometrically, it is as if this was the case within the cohomological point of view, which is consistent with the theory of Grothendieck Motives. We deduce the padic factorization of the Zeta function of a smooth algebraic variety, possibly open, over a finite field, which is a key testing result of our methods.
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Other Information
http://mathoverflow.net/questions/13977/istheresomethinglikecechcohomologyforpadicvarieties
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