Explicit Coleman integration for curves
Files
First author draft
Date
2020-01-13
DOI
Authors
Balakrishnan, Jennifer
Tuitman, Jan
Version
First author draft
OA Version
Citation
J. Balakrishnan, J. Tuitman. 2020. "Explicit Coleman integration for curves." https://arxiv.org/pdf/1710.01673.pdf
Abstract
The Coleman integral is a p-adic line integral that plays a key role in computing
several important invariants in arithmetic geometry. We give an algorithm for explicit Coleman
integration on curves, using the algorithms of the second author [Tui16, Tui17] to compute the
action of Frobenius on p-adic cohomology. We present a collection of examples computed with
our implementation. This includes integrals on a genus 55 curve, where other methods do not
currently seem practical.