Journal of Algebraic Geometry

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

Author(s): Elmar Große-Klönne
Journal: J. Algebraic Geom. 14 (2005), 391-437.
Posted: March 28, 2005
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Abstract: We define Frobenius and monodromy operators on the de Rham cohomology of

-dagger spaces (rigid spaces with overconvergent structure sheaves) with strictly semistable reduction

, over a complete discrete valuation ring

of mixed characteristic. For this we introduce log rigid cohomology and generalize the so-called Hyodo-Kato isomorphism to versions for non-proper

, for non-perfect residue fields, for non-integrally defined coefficients, and for the various strata of

. We apply this to define and investigate crystalline structure elements on the de Rham cohomology of Drinfel'd's symmetric space

and its quotients. Our results are used in a critical way in the recent proof of the monodromy-weight conjecture for quotients of

given by de Shalit (2005).

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