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.References
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Bibliographic Information
- Gerd Faltings
- Affiliation: Max-Planck-Institut für Mathematik, Gottfried-Claren-Str. 26, 53225 Bonn, Germany
- Email: gerd@mpim-bonn.mpg.de
- Received by editor(s): February 22, 1994
- Received by editor(s) in revised form: April 3, 1998
- © Copyright 1999 American Mathematical Society
- Journal: J. Amer. Math. Soc. 12 (1999), 117-144
- MSC (1991): Primary 14F30, 14L05
- DOI: https://doi.org/10.1090/S0894-0347-99-00273-8
- MathSciNet review: 1618483