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Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)



Integral crystalline cohomology
over very ramified valuation rings

Author: Gerd Faltings
Journal: J. Amer. Math. Soc. 12 (1999), 117-144
MSC (1991): Primary 14F30, 14L05
MathSciNet review: 1618483
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Abstract: We explain how to set up an integral version ($\mathbb{Z}_{p}$ as opposed to $\mathbb{Q}_{p}$) of Fontaine's comparison between crystalline and étale cohomology, over $p$-adic fields with arbitrary ramification index. The main results then are that Fontaine's map respects integrality of Tate-cycles, and a construction of versal deformations of $p$-divisible groups with Tate-cycles. An appendix deals with finite generation of crystalline cohomology.

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Gerd Faltings
Affiliation: Max-Planck-Institut für Mathematik, Gottfried-Claren-Str. 26, 53225 Bonn, Germany

Keywords: $p$-adic \'etale cohomology, crystalline cohomology, $p$-divisible groups
Received by editor(s): February 22, 1994
Received by editor(s) in revised form: April 3, 1998
Article copyright: © Copyright 1999 American Mathematical Society