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Equivariant crystalline cohomology and base change

Author: Elmar Grosse-Klönne
Journal: Proc. Amer. Math. Soc. 135 (2007), 1249-1253
MSC (2000): Primary 14F30, 13Dxx
Published electronically: October 18, 2006
MathSciNet review: 2276631
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Abstract: Given a perfect field $ k$ of characteristic $ p>0$, a smooth proper $ k$-scheme $ Y$, a crystal $ E$ on $ Y$ relative to $ W(k)$ and a finite group $ G$ acting on $ Y$ and $ E$, we show that, viewed as a virtual $ k[G]$-module, the reduction modulo $ p$ of the crystalline cohomology of $ E$ is the de Rham cohomology of $ E$ modulo $ p$. On the way we prove a base change theorem for the virtual $ G$-representations associated with $ G$-equivariant objects in the derived category of $ W(k)$-modules.

References [Enhancements On Off] (What's this?)

  • 1. Pierre Berthelot and Arthur Ogus, Notes on crystalline cohomology, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1978. MR 0491705
  • 2. Marc Cabanes and Michel Enguehard, Representation theory of finite reductive groups, New Mathematical Monographs, vol. 1, Cambridge University Press, Cambridge, 2004. MR 2057756
  • 3. E. Grosse-Klönne, On the crystalline cohomology of Deligne-Lusztig varieties, to appear in Finite Fields and Their Applications.

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Additional Information

Elmar Grosse-Klönne
Affiliation: Mathematisches Institut der Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany

Keywords: Crystalline cohomology, base change, virtual representation
Received by editor(s): February 15, 2005
Received by editor(s) in revised form: November 21, 2005
Published electronically: October 18, 2006
Communicated by: Michael Stillman
Article copyright: © Copyright 2006 American Mathematical Society

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