I'll introduce a variant of Arthur's truncation for a reductive group and its Lie algebra over a global function field inspired by reduction theory of flagged principal bundles. For some restricted test functions, we're able to pass from group case to Lie algebra. Using this construction, we can reduce the counting problem of Hitchin pairs to the counting of nilpotent pairs. We show this count has a relation with the dimension of the space of some automorphic forms. For general linear groups, it proves some cases of Deligne's conjecture by using Langlands correspondence proved by Lafforgue.
On a variant of Arthur's truncation and its applications
17.03.2020 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location:
Zoom ID: 431 655 310