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

Timo Keller; Michael Stoll

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arXiv · 2107.00325

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

Timo Keller·Michael Stoll

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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 $J$.

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Timo Keller, Michael Stoll. 2021-07-01. Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces. https://arxiv.org/abs/2107.00325

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