Galois cohomology of elliptic curves over anticyclotomic extensions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909855770476544 |
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| author | Nguyen, Dac-Nhan-Tam Ramdorai, Sujatha |
| author_facet | Nguyen, Dac-Nhan-Tam Ramdorai, Sujatha |
| contents | Let $K$ be an imaginary quadratic field and $p$ be an odd prime number. Let $E/\mathbb{Q}$ be an elliptic curve with good ordinary reduction at $p$. We study the Iwasawa theory of $E$ over the anticyclotomic $\mathbb{Z}_p$-extension of $K$ by adopting a unifying framework. We also study the Galois cohomology of the dual Selmer group of $E$ over the unique $\mathbb{Z}_p^2$-extension of $K$ as well as over the anticyclotomic extension of $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11835 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Galois cohomology of elliptic curves over anticyclotomic extensions Nguyen, Dac-Nhan-Tam Ramdorai, Sujatha Number Theory 11G05 (Primary) 11R23, 11R34 (Secondary) Let $K$ be an imaginary quadratic field and $p$ be an odd prime number. Let $E/\mathbb{Q}$ be an elliptic curve with good ordinary reduction at $p$. We study the Iwasawa theory of $E$ over the anticyclotomic $\mathbb{Z}_p$-extension of $K$ by adopting a unifying framework. We also study the Galois cohomology of the dual Selmer group of $E$ over the unique $\mathbb{Z}_p^2$-extension of $K$ as well as over the anticyclotomic extension of $K$. |
| title | Galois cohomology of elliptic curves over anticyclotomic extensions |
| topic | Number Theory 11G05 (Primary) 11R23, 11R34 (Secondary) |
| url | https://arxiv.org/abs/2508.11835 |