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

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

2006-09-22

arxiv.org/abs/math/0609645v3

Mathematics

Number Theory

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

Scientific paper

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.

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