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Local and global structure of connections on nonarchimedean curves

Published online by Cambridge University Press:  07 January 2015

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.

Type
Research Article
Copyright
© The Author 2015 

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