Timeline for Global Langlands function fields
Current License: CC BY-SA 3.0
6 events
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| Apr 4, 2020 at 3:12 | comment | added | Dr. Evil | Thanks for the reply. Can you remind us please what are the purity properties for GL_n? Also, what are the references for Arthur's multiplicity formula? Arthur's original papers are rather technical, so I'm hoping there is a review article out there, skipping the proofs but giving the basic ideas. Also, Arthur is usually dealing with number fields. I imagine the situation is simpler over function fields. Is that explained somewhere? | |
| Apr 3, 2020 at 13:00 | comment | added | Will Sawin | @Dr.Evil I'm not really an expert on this, but the Arthur multiplicity formula describes how many automorphic form correspond to a given Galois representation, and which automorphic representations they appear in. In $GL_n$, the answer is on automorphic form in one representation, as long as the Galois representations have the purity properties that mean we expect it to come from an automorphic form at all. For general groups $G$, the answer is more complicated, and involves calculating with representations of the centralizer in $G$ of the image of Galois. | |
| Apr 3, 2020 at 4:32 | comment | added | Dr. Evil | Is it possible to give a flavour of what the Arthur multiplicity formula says? | |
| Nov 23, 2017 at 3:21 | vote | accept | CommunityBot | ||
| Aug 16, 2017 at 12:22 | vote | accept | CommunityBot | ||
| Nov 23, 2017 at 3:21 | |||||
| Aug 15, 2017 at 19:14 | history | answered | Will Sawin | CC BY-SA 3.0 |