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Local solutions to positive characteristic non-Archimedean differential equations

Published online by Cambridge University Press:  01 November 2007

João Pedro Pinto dos Santos*
Affiliation:
IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes, France (email: [email protected])
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2007

References

This work is part of the author’s Cambridge PhD thesis supervised by N. I. Shepherd-Barron and financially supported by Trinity College.