Coleman integration using the Tannakian formalism

Amnon Besser

doi:10.1007/s002080100263

Coleman integration using the Tannakian formalism

Amnon Besser

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

We use a new idea to construct a theory of iterated Coleman functions on overconvergent spaces with good reduction in any dimension. A Coleman function in this theory consists of a unipotent differential equation, a functional on the underlying bundle and a solution to the equation on a residue class. The new idea is to use the theory of Tannakian categories and the action of Frobenius to analytically continue solutions of the differential equation to all residue classes.

Original language	English
Pages (from-to)	19-48
Number of pages	30
Journal	Mathematische Annalen
Volume	322
Issue number	1
DOIs	https://doi.org/10.1007/s002080100263
State	Published - 1 Dec 2002

ASJC Scopus subject areas

General Mathematics

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abstract = "We use a new idea to construct a theory of iterated Coleman functions on overconvergent spaces with good reduction in any dimension. A Coleman function in this theory consists of a unipotent differential equation, a functional on the underlying bundle and a solution to the equation on a residue class. The new idea is to use the theory of Tannakian categories and the action of Frobenius to analytically continue solutions of the differential equation to all residue classes.",

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AB - We use a new idea to construct a theory of iterated Coleman functions on overconvergent spaces with good reduction in any dimension. A Coleman function in this theory consists of a unipotent differential equation, a functional on the underlying bundle and a solution to the equation on a residue class. The new idea is to use the theory of Tannakian categories and the action of Frobenius to analytically continue solutions of the differential equation to all residue classes.

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Coleman integration using the Tannakian formalism

Abstract

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