Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces
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 $\Sha (J/\mathbb{Q})$ is trivial. This verifies the strong BSD conjecture for $J$.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2022-05-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.313/ |