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.
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