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Duality in the cohomology of crystalline local systems

Published online by Cambridge University Press:  04 December 2007

WIESŁAWA NIZIOL
WIESŁAWA NIZIOL
Affiliation:
The University of Chicago, Department of Mathematics, 5734 University Avenue, Chicago, Illinois 60637. e-mail: niziol@math.uchicago.edu
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Abstract

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Let $k$ be a perfect field of a positive characteristic $p, K$ – the fraction field of the ring of Witt vectors $W(k)$. Let $X$ be a smooth and proper scheme over $W(k)$. We present a candidate for a cohomology theory with coefficients in crystalline local systems: $p$-adic étale local systems on $X_K$ characterized by associating to them so called Fontaine-crystals on the crystalline site of the special fiber $X_k$. We show that this cohomology satysfies a duality theorem.

Keywords

crystalline local systemsduality
Type
Research Article
Information
Compositio Mathematica , Volume 109 , Issue 1 , October 1997 , pp. 67 - 97
Copyright
© 1997 Kluwer Academic Publishers