Mathematics – Number Theory
Scientific paper
2007-12-20
Mathematics
Number Theory
68 pages; v4: final refereed version; new section A.2; changes in 2.5 and throughout section 5
Scientific paper
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 0. 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.
No associations
LandOfFree
Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-3008