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