Timeline for What are the local Langlands conjectures nowadays, for connected reductive groups over a $p$-adic field?
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| Feb 10, 2010 at 7:48 | comment | added | Marty | I did misunderestimate :) - sorry! Vogan's treatment is the only one - or the first one, at least - to use perverse sheaves in the p-adic setting. As Ben-Zvi states below, it seems like the best way to understand not only the irreducibles, but also the structure of the category. From my perspective, Bernstein's center produces a complex variety, which "roughly" parameterizes representations. For each component in this variety, one should do something like Vogan to study the category of representations supported on this component. | |
| Feb 9, 2010 at 22:46 | comment | added | Kevin Buzzard | "...perverse sheaves (which the OP may or may not like)". Aah you misunderstand. What I was objecting to was not the perverse sheaves, but the fact that the perverse sheaves were always on a space that was introduced just after the fateful words "now let's assume we're in an equicharacteristic setting". On the other hand I see that Vogan introduces a space in the p-adic setting too, so I am cautiously optimistic... | |
| Feb 9, 2010 at 22:32 | history | answered | Marty | CC BY-SA 2.5 |