Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuations
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Kedlaya_Semistable Reduction (arxiv).pdf
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716.34 KB
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Author(s)
Kedlaya, Kiran S.
Date Issued
February 2011
Journal
Compositio Mathematica
Publisher
Cambridge University Press
Citation
Kedlaya, Kiran S. “Semistable Reduction for Overconvergent F-isocrystals, IV: Local Semistable Reduction at Nonmonomial Valuations.” Compositio Mathematica (2011): 1–57. Web.
Version
Author's final manuscript
Abstract
We complete our proof that given an overconvergent F-isocrystal on a variety over a field of positive characteristic, one can pull back along a suitable generically finite cover to obtain an isocrystal which extends, with logarithmic singularities and nilpotent residues, to some complete variety. We also establish an analogue for F-isocrystals overconvergent inside a partial compactification. By previous results, this reduces to solving a local problem in a neighborhood of a valuation of height 1 and residual transcendence degree zero. We do this by studying the variation of some numerical invariants attached to p-adic differential modules, analogous to the irregularity of a complex meromorphic connection. This allows for an induction on the transcendence defect of the valuation, i.e., the discrepancy between the dimension of the variety and the rational rank of the valuation.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1112/s0010437x10005142
