Coleman integration using the Tannakian formalism, by Amnon Besser

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.

Amnon Besser <bessera@math.bgu.ac.il>