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Semistable reduction for overconvergent F-isocrystals, II: A valuation-theoretic approach

Part of: (Co)homology theory

Published online by Cambridge University Press:  01 May 2008

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 introduce a valuation-theoretic approach to the problem of semistable reduction (i.e. existence of logarithmic extensions on suitable covers) of overconvergent isocrystals with Frobenius structure. The key tool is the quasicompactness of the Riemann–Zariski space associated to the function field of a variety. We also make some initial reductions, which allow attention to be focused on valuations of height 1 and transcendence degree 0.

Keywords

rigid cohomologyoverconvergent isocrystalssemistable reductionvaluationsRiemann–Zariski spaces

MSC classification

Secondary: 14F30: $p$-adic cohomology, crystalline cohomology 14F40: de Rham cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 3 , May 2008 , pp. 657 - 672
Copyright
Copyright © Foundation Compositio Mathematica 2008

References

The author was supported by NSF grant DMS-0400727.