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

Abstract

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