Semistable reduction for overconvergent, F-isocrystals, III: Local semistable reduction at monomial valuations
We resolve the local semistable reduction problem for overconvergent F-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 a p-adic differential modu...
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Format: | Article |
Language: | en_US |
Published: |
Cambridge University Press / Foundation Compositio Mathematica
2011
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Online Access: | http://hdl.handle.net/1721.1/62306 |
Summary: | We resolve the local semistable reduction problem for overconvergent F-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 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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