Explicit Coleman integration for curves
Number Theory
2020-05-29 v4 Algebraic Geometry
Abstract
The Coleman integral is a -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 to compute the action of Frobenius on -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.
Keywords
Cite
@article{arxiv.1710.01673,
title = {Explicit Coleman integration for curves},
author = {Jennifer S. Balakrishnan and Jan Tuitman},
journal= {arXiv preprint arXiv:1710.01673},
year = {2020}
}
Comments
Updated Assumption 2.6 (4), with thanks to Floris Vermeulen for bringing this to our attention