Semistable reduction for overconvergent F-isocrystals, IV: local semistable reduction at nonmonomial valuations

By Kiran S. Kedlaya. Compositio Mathematica, 2006

57 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/40c5b9b6e127e2cbff8ecf1bdceefcde145c19e0

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In Applied Mathematics

  1. Kiran S. Kedlaya
  2. Kentaro Nakamura
  3. Ruochuan Liu

In Computational Theory and Mathematics

  1. Kiran S. Kedlaya
  2. Alan G. B. Lauder
  3. T. Mochizuki
  4. Ruochuan Liu
  5. David Lubicz
  6. Reynald Lercier

In Geometry and Topology

  1. Kiran S. Kedlaya
  2. Ruochuan Liu
  3. Peter Scholze
  4. Alan G. B. Lauder
  5. T. Mochizuki
  6. Jonathan Pottharst
  7. Tomoyuki Abe
  8. David Lubicz

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