Timeline for Potential automorphy of abelian varieties
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 23, 2017 at 21:16 | answer | added | Joël | timeline score: 2 | |
| Nov 23, 2017 at 18:08 | answer | added | More of a comment | timeline score: 0 | |
| Nov 21, 2017 at 15:53 | comment | added | guest | @WillSawin: Oh, so maybe it is not relevant. That raises the question: are (1) and (2) related at all? | |
| Nov 21, 2017 at 7:59 | comment | added | Will Sawin | @guest I don't see how the Artin conjecture for $L(\chi,s)$ implies anything about the tensor product $L$-function $L(A \otimes \chi,s)$. | |
| Nov 21, 2017 at 2:22 | comment | added | guest | @reuns: the question is for general $A$. But suppose $K$ is totally real and $A$ is an abelian surface over $K$ with everywhere good reduction. So we can assume $\rho$ is unramified outside of primes dividing $\ell$. | |
| Nov 21, 2017 at 2:19 | comment | added | guest | @WillSawin: Because the L-function of $A$ over any Galois extension $K'$ of $K$ will be a product of the L-function $L(A \otimes \chi, s)$ where $\chi$ is an irreducible representation of the finite Galois group $\mathrm{Gal}(K'/K)$. So it seemed the Artin conjecture for $\chi$ might be relevant here. | |
| Nov 20, 2017 at 18:59 | comment | added | reuns | No assumptions but plenty of results have been proven, so please remind us (for those who know Artin L-functions better than abelian varieties) | |
| Nov 20, 2017 at 18:49 | comment | added | guest | @reuns: No assumptions on $\rho$. | |
| Nov 20, 2017 at 9:56 | comment | added | Will Sawin | Why do you think the Artin conjecture is relevant? | |
| Nov 20, 2017 at 4:20 | comment | added | reuns | Could you tell what results you assume about $\rho : \text{Gal}(\overline{K}/K) \to \text{Aut}(T_{\ell}(A))$ ? | |
| Nov 19, 2017 at 21:07 | history | asked | guest | CC BY-SA 3.0 |