Explicit Coleman integration for curves
MetadataShow full item record
First author draft
Citation (published version)J. Balakrishnan, J. Tuitman. 2020. "Explicit Coleman integration for curves." https://arxiv.org/pdf/1710.01673.pdf
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.