On the Pseudonullity of Fine Selmer groups over function fields
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909590336045056 |
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| author | Ghosh, Sohan |
| author_facet | Ghosh, Sohan |
| contents | The $p^\infty$-fine Selmer group of an elliptic curve $E$ over a global field is a subgroup of the classical $p^\infty$-Selmer group. Coates and Sujatha discovered that the structure of the fine Selmer group of $E$ over certain $p$-adic Lie extensions of a number field is intricately related to some deep questions in classical Iwasawa theory. Inspired by a conjecture of Greenberg, they made prediction about the structure of the fine Selmer group over certain $p$-adic Lie extensions of a number field, which they called Conjecture B. In this article, we discuss some new cases of Conjecture B and its analogues over some $p$-adic Lie extensions of function fields of characteristic $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00499 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Pseudonullity of Fine Selmer groups over function fields Ghosh, Sohan Number Theory The $p^\infty$-fine Selmer group of an elliptic curve $E$ over a global field is a subgroup of the classical $p^\infty$-Selmer group. Coates and Sujatha discovered that the structure of the fine Selmer group of $E$ over certain $p$-adic Lie extensions of a number field is intricately related to some deep questions in classical Iwasawa theory. Inspired by a conjecture of Greenberg, they made prediction about the structure of the fine Selmer group over certain $p$-adic Lie extensions of a number field, which they called Conjecture B. In this article, we discuss some new cases of Conjecture B and its analogues over some $p$-adic Lie extensions of function fields of characteristic $p$. |
| title | On the Pseudonullity of Fine Selmer groups over function fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2304.00499 |