Abstract

Let C be a smooth projective curve over a number field. To verify numerically Birch and Swinnerton-Dyer's conjecture for the Jacobian of C,  we have to compute explicitly some local arithmetic invariants of C such as the volume form, Tamagawa numbers, and Euler factors.  In this talk, I will explain how to simplify the computation for some hyperelliptic curves, especially for curves of genus 2.