Vol. 1, No. 1, 2013

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Iterated Coleman integration for hyperelliptic curves

Jennifer S. Balakrishnan

Vol. 1 (2013), No. 1, 41–61
Abstract

The Coleman integral is a p-adic line integral. Double Coleman integrals on elliptic curves appear in Kim’s nonabelian Chabauty method, the first numerical examples of which were given by the author, Kedlaya, and Kim. This paper describes the algorithms used to produce those examples, as well as techniques to compute higher iterated integrals on hyperelliptic curves, building on previous joint work with Bradshaw and Kedlaya.

Keywords
Coleman integration, $p$-adic integration, iterated Coleman integration, hyperelliptic curves, nonabelian Chabauty, integral points
Mathematical Subject Classification 2010
Primary: 11S80
Secondary: 11Y35, 11Y50
Milestones
Published: 14 November 2013
Authors
Jennifer S. Balakrishnan
Department of Mathematics
Harvard University
1 Oxford Street
Cambridge, MA 02138, USA