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Local and global structure of connections on nonarchimedean curves

Part of: Arithmetic problems. Diophantine geometry Differential and difference algebra

Published online by Cambridge University Press:  07 January 2015

Kiran S. Kedlaya
Kiran S. Kedlaya*
Affiliation:
Department of Mathematics, University of California, San Diego, 9500 Gilman Drive #0112, La Jolla, CA 92093, USA email kedlaya@ucsd.edu
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Abstract

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Consider a vector bundle with connection on a $p$-adic analytic curve in the sense of Berkovich. We collect some improvements and refinements of recent results on the structure of such connections, and on the convergence of local horizontal sections. This builds on work from the author’s 2010 book and on subsequent improvements by Baldassarri and by Poineau and Pulita. One key result exclusive to this paper is that the convergence polygon of a connection is locally constant around every type 4 point.

Keywords

p-adic differential equationsradius of convergenceconvergence polygonnonarchimedean analytic spaces

MSC classification

Primary: 12H25: $p$-adic differential equations 14G22: Rigid analytic geometry
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 6 , June 2015 , pp. 1096 - 1156
Copyright
© The Author 2015 

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