Equivariant crystalline cohomology and base change
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- by Elmar Grosse-Klönne PDF
- Proc. Amer. Math. Soc. 135 (2007), 1249-1253 Request permission
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
- Pierre Berthelot and Arthur Ogus, Notes on crystalline cohomology, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1978. MR 0491705
- Marc Cabanes and Michel Enguehard, Representation theory of finite reductive groups, New Mathematical Monographs, vol. 1, Cambridge University Press, Cambridge, 2004. MR 2057756, DOI 10.1017/CBO9780511542763
- E. Grosse-Klönne, On the crystalline cohomology of Deligne-Lusztig varieties, to appear in Finite Fields and Their Applications.
Additional Information
- Elmar Grosse-Klönne
- Affiliation: Mathematisches Institut der Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany
- Email: klonne@math.uni-muenster.de
- 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
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 1249-1253
- MSC (2000): Primary 14F30, 13Dxx
- DOI: https://doi.org/10.1090/S0002-9939-06-08634-5
- MathSciNet review: 2276631