Heidelberg lectures on coleman integration

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4 Scopus citations

Abstract

Coleman integration is a way of associating with a closed one-form on a p-adic space a certain locally analytic function, defined up to a constant, whose differential gives back the form. This theory, initially developed by Robert Coleman in the 1980s and later extended by various people including the author, has now found various applications in arithmetic geometry, most notably in the spectacular work of Kim on rational points. In this text we discuss two approaches to Coleman integration, the first is a semi-linear version of Coleman’s original approach, which is better suited for computations. The second is the author’s approach via unipotent isocrystals, with a simplified and essentially self-contained presentation. We also survey many applications of Coleman integration and describe a new theory of integration in families.

Original languageEnglish
Title of host publicationThe Arithmetic of Fundamental Groups
Subtitle of host publicationPIA 2010
PublisherSpringer Berlin Heidelberg
Pages3-52
Number of pages50
ISBN (Electronic)9783642239052
ISBN (Print)9783642239045
DOIs
StatePublished - 1 Jan 2012

ASJC Scopus subject areas

  • Mathematics (all)

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