Explicit Coleman integration for hyperelliptic curves

Abstract

Coleman's theory of p-adic integration figures prominently in several number-theoretic applications, such as finding torsion and rational points on curves, and computing p-adic regulators in K-theory (including p-adic heights on elliptic curves). We describe an algorithm for computing Coleman integrals on hyperelliptic curves, and its implementation in Sage.

16 pages; v2: final submission to ANTS 9

References in corpus (1)

• Counting Points on Hyperelliptic Curves using Monsky-Washnitzer Cohomology

Cited by in corpus (4)

• A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties
• A non-abelian conjecture of Tate-Shafarevich type for hyperbolic curves
• Quadratic Chabauty: p-adic height pairings and integral points on hyperelliptic curves
• Computing integral points on hyperelliptic curves using quadratic Chabauty