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
Full-text PDF

Abstract | References | Additional Information

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).

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

Additional Information

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

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
AMS Website