The p-adic local monodromy theorem for fake annuli
نویسنده
چکیده
We establish a generalization of the p-adic local monodromy theorem (of André, Mebkhout, and the author) in which differential equations on rigid analytic annuli are replaced by differential equations on so-called “fake annuli”. The latter correspond loosely to completions of a Laurent polynomial ring with respect to a monomial valuation. The result represents a step towards a higher-dimensional version of the p-adic local monodromy theorem (the “problem of semistable reduction”); it can also be viewed as a novel presentation of the original p-adic local monodromy theorem.
منابع مشابه
A ug 2 00 5 The p - adic local monodromy theorem for fake annuli , I : The monomial case
We establish a generalization of the p-adic local monodromy theorem (of André, Mebkhout, and the author) in which differential equations on rigid analytic annuli are replaced by differential equations on so-called “fake annuli”. The latter correspond loosely to completions of a Laurent polynomial ring with respect to a valuation, which in this paper is restricted to be of monomial form; we defe...
متن کاملSemistable 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 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...
متن کاملSemistable reduction for overconvergent, F-isocrystals, III: Local semistable reduction at monomial valuations Citation
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-a...
متن کاملLocal monodromy of p-adic differential equations: an overview
This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a p-adic (rigid analytic) annulus, though often with simpler proofs. These include Matsuda’s classification of quasiunipotent ∇-modules, the Christol-Mebkhout construction of the ramification filtration, and the Christol-Dwork Frobenius antecedent theorem. We also ...
متن کاملA p-adic local monodromy theorem
We prove a local monodromy theorem for p-adic differential equations on an annulus, answering a question of R. Crew. Specifically, suppose given a finite free module over the Robba ring (the ring of germs of functions analytic on some open p-adic annulus with outer radius 1) with a connection and a compatible Frobenius structure. We prove that the module admits a basis over a finite extension o...
متن کامل