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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Frobenius and monodromy operators in rigid analysis, and Drinfel’d’s symmetric space

Author: Elmar Große-Klönne
Journal: J. Algebraic Geom. 14 (2005), 391-437
Published electronically: March 28, 2005
MathSciNet review: 2129006
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Abstract: We define Frobenius and monodromy operators on the de Rham cohomology of $K$-dagger spaces (rigid spaces with overconvergent structure sheaves) with strictly semistable reduction $Y$, over a complete discrete valuation ring $K$ of mixed characteristic. For this we introduce log rigid cohomology and generalize the so-called Hyodo-Kato isomorphism to versions for non-proper $Y$, for non-perfect residue fields, for non-integrally defined coefficients, and for the various strata of $Y$. We apply this to define and investigate crystalline structure elements on the de Rham cohomology of Drinfel’d’s symmetric space $X$ and its quotients. Our results are used in a critical way in the recent proof of the monodromy-weight conjecture for quotients of $X$ given by de Shalit (2005).

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

Received by editor(s): April 18, 2003
Received by editor(s) in revised form: October 15, 2004
Published electronically: March 28, 2005
Additional Notes: Partly supported by Deutsche Forschungs Gemeinschaft