Rank Jumps and Growth of Shafarevich--Tate Groups for Elliptic Curves in $\mathbb{Z}/p\mathbb{Z}$-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_ | 1866917574823903232 |
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| author | Beneish, Lea Kundu, Debanjana Ray, Anwesh |
| author_facet | Beneish, Lea Kundu, Debanjana Ray, Anwesh |
| contents | In this paper, we use techniques from Iwasawa theory to study questions about rank jump of elliptic curves in cyclic extensions of prime degree. We also study growth of the $p$-primary Selmer group and the Shafarevich--Tate group in cyclic degree-$p$ extensions and improve upon previously known results in this direction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_09166 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Rank Jumps and Growth of Shafarevich--Tate Groups for Elliptic Curves in $\mathbb{Z}/p\mathbb{Z}$-Extensions Beneish, Lea Kundu, Debanjana Ray, Anwesh Number Theory 11G05, 11R23, 11R34 In this paper, we use techniques from Iwasawa theory to study questions about rank jump of elliptic curves in cyclic extensions of prime degree. We also study growth of the $p$-primary Selmer group and the Shafarevich--Tate group in cyclic degree-$p$ extensions and improve upon previously known results in this direction. |
| title | Rank Jumps and Growth of Shafarevich--Tate Groups for Elliptic Curves in $\mathbb{Z}/p\mathbb{Z}$-Extensions |
| topic | Number Theory 11G05, 11R23, 11R34 |
| url | https://arxiv.org/abs/2107.09166 |