Timeline for References for Artin motives
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 17, 2010 at 4:53 | comment | added | Anweshi | @Emerton. Can we recover a number field from the knowledge of Artin motives attached to it? In general, is it possible to recover an algebraic variety from a motivic understanding, i. e., is it possible to get back to the original thing, if you know the motivic chunks as you called them? | |
| Jan 16, 2010 at 22:38 | comment | added | Emerton | If you like. The adjective Artin comes from the use of Artin representation to describe Galois representations into GL_n(C) (where here C is the complex numbers, but could be any field of char. zero). Artin motives are to all motives as Artin representations are to all (ell-adic, say) Galois representations. | |
| Jan 16, 2010 at 21:24 | comment | added | Anweshi | @Emerton. So are Artin motives just another way of looking at Galois representations defined over number fields? | |
| Jan 16, 2010 at 20:16 | comment | added | Anweshi | @Emerton. Your answer was extremely helpful to me, and it was very enlightening to read it. However I am accepting YBL's answer since I had asked for references and he gave me some. I hope you don't mind. | |
| Jan 16, 2010 at 4:02 | comment | added | Emerton | The case of 2-dimensional odd representations, in the case $K = {\mathbb Q}$, follows from Khare--Wintenberger--Kisin. This is an example of one of the ``very few non-abelian cases'' that are known. | |
| Jan 16, 2010 at 3:07 | comment | added | Anweshi | The conjecture on Artin L-functions does not follow from Khare's work on Serre's conjectures? | |
| Jan 16, 2010 at 2:50 | comment | added | Anweshi | Thanks, this was very helpful. As I mentioned, the aim was to get to the equivariant Tamagawa number conjecture. Are there any specific suggestions towards that? | |
| Jan 16, 2010 at 2:47 | history | answered | Emerton | CC BY-SA 2.5 |