On the unramified Iwasawa module of a $\mathbb{Z}_p$-extension generated by division points of a CM elliptic curve
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911969722761216 |
|---|---|
| author | Itoh, Tsuyoshi |
| author_facet | Itoh, Tsuyoshi |
| contents | We consider the unramified Iwasawa module $X (F_\infty)$ of a certain $\mathbb{Z}_p$-extension $F_\infty/F_0$ generated by division points of an elliptic curve with complex multiplication. This $\mathbb{Z}_p$-extension has properties similar to those of the cyclotomic $\mathbb{Z}_p$-extension of a real abelian field, however, it is already known that $X (F_\infty)$ can be infinite. That is, an analog of Greenberg's conjecture for this $\mathbb{Z}_p$-extension fails. In this paper, we mainly consider analogs of weak forms of Greenberg's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_04687 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the unramified Iwasawa module of a $\mathbb{Z}_p$-extension generated by division points of a CM elliptic curve Itoh, Tsuyoshi Number Theory 11R23 (11G05, 11G15) We consider the unramified Iwasawa module $X (F_\infty)$ of a certain $\mathbb{Z}_p$-extension $F_\infty/F_0$ generated by division points of an elliptic curve with complex multiplication. This $\mathbb{Z}_p$-extension has properties similar to those of the cyclotomic $\mathbb{Z}_p$-extension of a real abelian field, however, it is already known that $X (F_\infty)$ can be infinite. That is, an analog of Greenberg's conjecture for this $\mathbb{Z}_p$-extension fails. In this paper, we mainly consider analogs of weak forms of Greenberg's conjecture. |
| title | On the unramified Iwasawa module of a $\mathbb{Z}_p$-extension generated by division points of a CM elliptic curve |
| topic | Number Theory 11R23 (11G05, 11G15) |
| url | https://arxiv.org/abs/2001.04687 |