Integral crystalline cohomology over very ramified valuation rings

Faltings, Gerd

doi:10.1090/S0894-0347-99-00273-8

Integral crystalline cohomology over very ramified valuation rings
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by Gerd Faltings

J. Amer. Math. Soc. 12 (1999), 117-144

DOI: https://doi.org/10.1090/S0894-0347-99-00273-8

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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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