Vol. 2, 2019

Download this article
Download this article For screen
For printing
Recent Volumes
4: ANTS XIV
3: Hillman: Poincaré Duality
2: ANTS XIII
1: ANTS X
The Open Book Series
All Volumes
 
About the Series
Ethics Statement
Purchase Printed Copies
Author Index
 
MSP Books and Monographs
Other MSP Publications
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