Local-global compatibility over function fields
Number Theory
2023-08-15 v2 Algebraic Geometry
Representation Theory
Abstract
We prove that V. Lafforgue's global Langlands correspondence is compatible with Fargues-Scholze's semisimplified local Langlands correspondence. As a consequence, we canonically lift Fargues-Scholze's construction to a non-semisimplified local Langlands correspondence for positive characteristic local fields. We also deduce that Fargues-Scholze's construction agrees with that of Genestier-Lafforgue, answering a question of Fargues-Scholze, Hansen, Harris, and Kaletha. The proof relies on a uniformization morphism for moduli spaces of shtukas.
Cite
@article{arxiv.2301.09711,
title = {Local-global compatibility over function fields},
author = {Siyan Daniel Li-Huerta},
journal= {arXiv preprint arXiv:2301.09711},
year = {2023}
}
Comments
Removed restrictions on $p$ in Theorem B and fixed minor errors. 54 pages. Comments welcome!