On the Mordell-Weil Ranks of supersingular abelian varieties over $\mathbb{Z}_p^2$-extensions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866910513053564928 |
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| author | Dion, Cédric Ray, Jishnu |
| author_facet | Dion, Cédric Ray, Jishnu |
| contents | Let $p$ be a fixed odd prime and let $K$ be an imaginary quadratic field in which $p$ splits. Let $A$ be an abelian variety defined over $K$ with supersingular reduction at both primes above $p$ in $K$. Under certain assumptions, we give a growth estimate for the Mordell--Weil rank of $A$ over finite extensions inside the $\mathbb{Z}_p^2$-extension of $K$. In the last section, written by Chris Williams, he includes some speculative remarks on the $p$-adic $L$-functions for $\mathrm{GSp}(4)$ corresponding to the multi-signed Selmer groups constructed in this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_00280 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the Mordell-Weil Ranks of supersingular abelian varieties over $\mathbb{Z}_p^2$-extensions Dion, Cédric Ray, Jishnu Number Theory Representation Theory Primary: 11R23. Secondary: 11G10, 11R20 Let $p$ be a fixed odd prime and let $K$ be an imaginary quadratic field in which $p$ splits. Let $A$ be an abelian variety defined over $K$ with supersingular reduction at both primes above $p$ in $K$. Under certain assumptions, we give a growth estimate for the Mordell--Weil rank of $A$ over finite extensions inside the $\mathbb{Z}_p^2$-extension of $K$. In the last section, written by Chris Williams, he includes some speculative remarks on the $p$-adic $L$-functions for $\mathrm{GSp}(4)$ corresponding to the multi-signed Selmer groups constructed in this paper. |
| title | On the Mordell-Weil Ranks of supersingular abelian varieties over $\mathbb{Z}_p^2$-extensions |
| topic | Number Theory Representation Theory Primary: 11R23. Secondary: 11G10, 11R20 |
| url | https://arxiv.org/abs/2112.00280 |