Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces

Timo Keller; Michael Stoll

Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces

Number Theory 2021-07-02 v1 Algebraic Geometry

Authors: Timo Keller , Michael Stoll

Abstract

Let $X$ be one of the $28$ Atkin-Lehner quotients of a curve $X_0(N)$ such that $X$ has genus $2$ and its Jacobian variety $J$ is absolutely simple. We show that the Shafarevich-Tate group of $J/\mathbb{Q}$ is trivial. This verifies the strong BSD conjecture for $J$ .

Keywords

strong bsd conjecture abelian surfaces shafarevich-tate group jacobian variety atkin-lehner quotients genus 2 curves

Cite

@article{arxiv.2107.00325,
  title  = {Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces},
  author = {Timo Keller and Michael Stoll},
  journal= {arXiv preprint arXiv:2107.00325},
  year   = {2021}
}

Comments

7 pages, details will be presented in a forthcoming article

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