Vol. 2, 2019

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Explicit Coleman integration in larger characteristic

Alex J. Best

Vol. 2 (2019), No. 1, 85–102
Abstract

We describe a more efficient algorithm to compute p-adic Coleman integrals on odd degree hyperelliptic curves for large primes p. The improvements come from using fast linear recurrence techniques when reducing differentials in Monsky–Washnitzer cohomology, a technique introduced by Harvey when computing zeta functions. The complexity of our algorithm is quasilinear in p and is polynomial in the genus and precision. We provide timings comparing our implementation with existing approaches.

Keywords
Coleman integration, hyperelliptic curves, Kedlaya's algorithm
Mathematical Subject Classification 2010
Primary: 11G20
Secondary: 11Y16, 14F30
Milestones
Received: 2 March 2018
Revised: 8 June 2018
Accepted: 9 September 2018
Published: 13 February 2019
Authors
Alex J. Best
Department of Mathematics and Statistics
Boston University
Boston, MA
United States