Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuations
Author(s)
Kedlaya, Kiran S.
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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.
Date issued
2011-02Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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
ISSN
0010-437X
1570-5846