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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Integral crystalline cohomology over very ramified valuation rings
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by Gerd Faltings
J. Amer. Math. Soc. 12 (1999), 117-144


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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Bibliographic Information
  • Gerd Faltings
  • Affiliation: Max-Planck-Institut für Mathematik, Gottfried-Claren-Str. 26, 53225 Bonn, Germany
  • Email:
  • 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:
  • MathSciNet review: 1618483