English

Semistable reduction for overconvergent F-isocrystals, III: Local semistable reduction at monomial valuations

Number Theory 2014-01-14 v3 Algebraic Geometry

Abstract

We resolve the local semistable reduction problem for overconvergent F-isocrystals at monomial valuations (Abhyankar valuations of height 1 and residue transcendence degree 0). We first introduce a higher-dimensional analogue of the generic radius of convergence for a p-adic differential module, which obeys a convexity property. We then combine this convexity property with a form of the p-adic local monodromy theorem for so-called fake annuli.

Keywords

Cite

@article{arxiv.math/0609645,
  title  = {Semistable reduction for overconvergent F-isocrystals, III: Local semistable reduction at monomial valuations},
  author = {Kiran S. Kedlaya},
  journal= {arXiv preprint arXiv:math/0609645},
  year   = {2014}
}

Comments

36 pages; v3: refereed version; adds appendix with two examples