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- W4367190610 abstract "Let $E$ be an elliptic curve over $mathbb{Q}$ with supersingular reduction at $p$ with $a_p=0$. We study the asymptotic growth of the plus and minus Tate-Shafarevich groups defined by Lei along the cyclotomic $mathbb{Z}_p$-extension of $mathbb{Q}$. In this paper, we work in the general framework of supersingular abelian varieties defined over $mathbb{Q}$. Using Coleman maps constructed by Buyukboduk--Lei, we define the multi-signed Mordell-Weil groups for supersingular abelian varieties, provide an explicit structure of the dual of these groups as an Iwasawa module and prove a control theorem. Furthermore, we define the multi-signed Tate-Shafarevich groups and, by computing their Kobayashi rank, we provide an asymptotic growth formula along the cyclotomic tower of $mathbb{Q}$." @default.
- W4367190610 created "2023-04-28" @default.
- W4367190610 creator A5042326537 @default.
- W4367190610 date "2023-04-26" @default.
- W4367190610 modified "2023-10-01" @default.
- W4367190610 title "Asymptotic growth of the signed Tate-Shafarevich groups for supersingular abelian varieties" @default.
- W4367190610 doi "https://doi.org/10.48550/arxiv.2304.13452" @default.
- W4367190610 hasPublicationYear "2023" @default.
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