Refined conjectures on Fitting ideals of Selmer groups over $\mathbf{Z}_p^2$-extensions
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914809683902464 |
|---|---|
| author | Dion, Cédric |
| author_facet | Dion, Cédric |
| contents | Let $p>3$ be a prime number and $K$ be an imaginary quadratic field where $p$ splits. Let $K_\infty$ be the $\mathbf{Z}_p^2$-extension of $K$ and let $K_n$ be a finite subextension of $K_\infty/K$. Let $E$ be an elliptic curve with good ordinary reduction at $p$. Under some hypotheses, we show that the Mazur-Tate element attached to $E$ over $K_n$ by S. Haran generates the Fitting ideal of the dual Selmer group of $E$ over $K_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15076 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Refined conjectures on Fitting ideals of Selmer groups over $\mathbf{Z}_p^2$-extensions Dion, Cédric Number Theory Let $p>3$ be a prime number and $K$ be an imaginary quadratic field where $p$ splits. Let $K_\infty$ be the $\mathbf{Z}_p^2$-extension of $K$ and let $K_n$ be a finite subextension of $K_\infty/K$. Let $E$ be an elliptic curve with good ordinary reduction at $p$. Under some hypotheses, we show that the Mazur-Tate element attached to $E$ over $K_n$ by S. Haran generates the Fitting ideal of the dual Selmer group of $E$ over $K_n$. |
| title | Refined conjectures on Fitting ideals of Selmer groups over $\mathbf{Z}_p^2$-extensions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2405.15076 |