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Local solutions to positive characteristic non-Archimedean differential equations
Published online by Cambridge University Press: 01 November 2007
Abstract
In the complex domain, one can integrate (solve) holomorphic ordinary differential equations (ODEs) near a non-singular point. We study the existence of solutions in the case of a positive characteristic base field k which is complete with respect to a non-Archimedean absolute value. ODEs are substituted by modules over a ring of analytic functions endowed with an action of all differential operators. The monodromy groups associated to the corresponding category are computed.
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- Copyright © Foundation Compositio Mathematica 2007
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This work is part of the author’s Cambridge PhD thesis supervised by N. I. Shepherd-Barron and financially supported by Trinity College.