2020/08/09 by Enis Kaya, Kaya, Enis
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #Polynomial and algebraic computation #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.2008.03774
Comments welcome!; v2: a new subsection called "Error Bounds'' added
openalex publication_date 2020/08/09 · arxiv created 2021/12/14 · arxiv updated 2021/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Vologodsky's theory of p-adic integration plays a central role in computing several interesting invariants in arithmetic geometry. In contrast with the theory developed by Coleman, it has the advantage of being insensitive to the reduction type at p. Building on recent work of Besser and Zerbes, we describe an algorithm for computing Vologodsky integrals on bad reduction hyperelliptic curves. This extends previous joint work with Katz to all meromorphic differential forms. We illustrate our algorithm with numerical examples computed in Sage.