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Semistable reduction for overconvergent F-isocrystals, III: Local semistable reduction at monomial valuations

Part of: (Co)homology theory

Published online by Cambridge University Press:  01 January 2009

Kiran S. Kedlaya
Kiran S. Kedlaya*
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA (email: kedlaya@mit.edu)
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Abstract

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We resolve the local semistable reduction problem for overconvergent F-isocrystals at monomial valuations (Abhyankar valuations of height 1 and residue transcendence degree zero). We first introduce a higher-dimensional analogue of the generic radius of convergence for a p-adic differential module, which obeys a convexity property. We then combine this convexity property with a form of the p-adic local monodromy theorem for so-called fake annuli.

Keywords

rigid cohomologyoverconvergent isocrystalssemistable reductionmonomial valuations

MSC classification

Secondary: 14F30: $p$-adic cohomology, crystalline cohomology 14F40: de Rham cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 1 , January 2009 , pp. 143 - 172
Copyright
Copyright © Foundation Compositio Mathematica 2009

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