Heidelberg Lectures on Coleman Integration

Conference paper
First Online:
Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 2)

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.

Keywords

Vector Bundle Hopf Algebra Short Exact Sequence Horizontal Section Torsion Point 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Ben-GurionUniversity of the NegevBe’er-ShevaIsrael

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