Modular functoriality in the Local Langlands Correspondence
Number Theory
2024-08-27 v3 Representation Theory
Abstract
We develop a theory of Smith-Treumann localization and relative parity sheaves in the context of Fargues-Scholze's Geometrization of the Local Langlands Correspondence. We then apply this theory to prove some conjectures of Treumann-Venkatesh concerning mod- Local Langlands functoriality between a reductive group and its fixed subgroup under an order automorphism. As another application, we calculate the Fargues-Scholze parameters of mod- Howe-unramified toral representations.
Cite
@article{arxiv.2312.12542,
title = {Modular functoriality in the Local Langlands Correspondence},
author = {Tony Feng},
journal= {arXiv preprint arXiv:2312.12542},
year = {2024}
}
Comments
Substantive corrections to Section 5, plus minor revisions elsewhere