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$p$-adic periods and derived de Rham cohomology


Author: A. Beilinson
Journal: J. Amer. Math. Soc. 25 (2012), 715-738
MSC (2010): Primary 14F30, 14F40; Secondary 14F20
DOI: https://doi.org/10.1090/S0894-0347-2012-00729-2
Published electronically: January 27, 2012
MathSciNet review: 2904571
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Abstract: We show that derived de Rham cohomology of Illusie satisfies the $p$-adic PoincarĂ© lemma in h-topology. This yields a new construction of the $p$-adic period map and a simple proof of Fontaine’s C$_{\text {dR}}$ conjecture.


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Additional Information

A. Beilinson
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
MR Author ID: 33735
Email: sasha@math.uchicago.edu

Keywords: $p$-Adic periods, derived de Rham cohomology, h-topology, alterations
Received by editor(s): February 22, 2011
Received by editor(s) in revised form: November 16, 2011, and January 5, 2012
Published electronically: January 27, 2012
Additional Notes: The author was supported in part by NSF grant DMS-1001660.
Dedicated: To Irene
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.