Number Theory Seminar

Title: Canonical heights on Jacobians of curves of genus two.

Speaker: Jan Steffen Müller, Univ. Oldenburg.

Abstract: To find explicit generators for the Mordell-Weil group of an abelian variety over a global field, one needs algorithms to compute canonical (i.e. N\'eron-Tate) heights of rational points and to enumerate all rational points of bounded canonical height. In my talk, I will discuss how this can be done efficiently for Jacobians of curves of genus 2. The idea is to decompose the difference between the canonical height and the corresponding naive height into a sum of local error functions. The non-archimedean local error functions can be analyzed using Picard functors and Zhang's theory of harmonic analysis on reduction graphs. This is joint work with Michael Stoll.