Coleman integration using the Tannakian formalism

Details Coleman integration using the Tannakian formalism Coleman integration using the Tannakian formalism

2000-11-02

arxiv.org/abs/math/0011269v1

Mathematics

Number Theory

Scientific paper

We use a new idea to construct a theory of iterated Coleman functions in higher dimensions than 1. A Coleman function in this theory consists of a unipotent differential equation, a section on the underlying bundle and a solution to the equation on a residue disc. The new idea is to use the theory of Tannakian categories and the action of Frobenius to anlytically continue solutions of the differential equation to all residue discs.

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