Timeline for Higher-dimensional Artin L-functions
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 20, 2015 at 10:52 | comment | added | Daniel Loughran | After chasing references, I have managed to find a proof of the result I want. It can be found in Section 2.1. of Faltings - Complements to Mordell. Thank you for your help on this matter. | |
| Oct 17, 2015 at 9:19 | vote | accept | Daniel Loughran | ||
| Oct 15, 2015 at 17:39 | comment | added | François Brunault | It would be also very nice to define a $G$-equivariant L-function in this setting. I have not seen a reference for this. This would not really be a new object, but this would tie things together nicely I think. | |
| Oct 15, 2015 at 17:34 | comment | added | François Brunault | It seems that Serre's inductive argument on the dimension to show $L(\rho,n) \neq 0$ could also be used on the line $\mathrm{Re}(s)=n$, but I'm really no expert here. Unfortunately I know of no other reference than this article. It would be indeed very nice to have a reference with more detailed proofs. | |
| Oct 15, 2015 at 16:21 | comment | added | Daniel Loughran | It is a shame that this paper contains essentially no proofs, especially of the interesting result you mention. Any idea where I can find proofs? | |
| Oct 15, 2015 at 16:20 | comment | added | Daniel Loughran | Thanks very much for the reference (I have now found a copy of it in English). In fact Serre mentions a result in his paper which is almost exactly the answer to Q2. Namely the final Corollary in the paper states that $L(s,\rho)$ is holomorphic and non-zero at $s=n$. I wonder if it is somehow implicit in this work that $L(s,\rho)$ is also holomorphic and non-zero on the line $\text{re}(s) = n$? | |
| Oct 15, 2015 at 14:40 | history | edited | François Brunault | CC BY-SA 3.0 |
added 126 characters in body
|
| Oct 15, 2015 at 14:23 | history | answered | François Brunault | CC BY-SA 3.0 |