Timeline for Kato's Euler System for Isogenous Elliptic Curves
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Dec 15, 2018 at 16:04 | comment | added | debanjana | Sujatha's recent paper with Witte (2017), solves it for the CM elliptic curves too and some other cases. We were curious if it is known/ if it is possible to translate isogeny invariance of Conjecture A (over Q) to the language of Euler systems and see if something can be said in general. | |
| Dec 15, 2018 at 0:16 | comment | added | Chris Wuthrich | @debanjana But Corollary 3.6 in their paper implies that, if $E$ has a $p$-isogeny defined over $\mathbb{Q}$, then Conjecture A is valid. So there is no need to use Kato's Euler system for this. The isogeny invariance of Conjecture A is only open for general number fields. | |
| Dec 13, 2018 at 18:21 | comment | added | debanjana | Thanks! As I understand, Euler systems "see" the fine Selmer group and therefore knowing isogeny invariance of Coates-Sujatha 'Conjecture A' for elliptic curves over $\mathbb{Q}$ should translate to understanding this question. | |
| Dec 13, 2018 at 9:16 | history | answered | Chris Wuthrich | CC BY-SA 4.0 |