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Differential modules on p-adic polyannuli

Part of: Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  19 May 2009

Kiran S. Kedlaya  and
Liang Xiao
Kiran S. Kedlaya
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA ([email protected])
Liang Xiao
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA ([email protected])
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Abstract

We consider variational properties of some numerical invariants, measuring convergence of local horizontal sections, associated to differential modules on polyannuli over a nonarchimedean field of characteristic 0. This extends prior work in the one-dimensional case of Christol, Dwork, Robba, Young, et al. Our results do not require positive residue characteristic; thus besides their relevance to the study of Swan conductors for isocrystals, they are germane to the formal classification of flat meromorphic connections on complex manifolds.

Keywords

differential modulespolyannulinonarchimedean fieldgeneric radius of convergence

MSC classification

Secondary: 14G22: Rigid analytic geometry
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 9 , Issue 1 , January 2010 , pp. 155 - 201
Copyright
Copyright © Cambridge University Press 2010

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