Birch and Swinnerton–Dyer conjecture for genus 2 Jacobians

Establish the Birch and Swinnerton–Dyer conjecture for the Jacobian of a genus 2 curve C over Q, relating arithmetic invariants of the Jacobian to the behavior of its L-function L(C,s).

Background

The Birch and Swinnerton–Dyer conjecture links the rank and other arithmetic invariants of an abelian variety to the analytic behavior of its L-function at s=1. For genus 2 curves, this concerns the Jacobian J(C) and L(C,s).

The authors note that L(C,s) is part of several major open conjectures, including BSD, and their algorithm aims to facilitate computations that are necessary for testing and proving instances in this setting.