Recent progress on Langlands reciprocity for $\mathrm{GL}_n$: Shimura varieties and beyond
Number Theory
2023-11-23 v1
Abstract
The goal of these lecture notes is to survey progress on the global Langlands reciprocity conjecture for over number fields from the last decade and a half. We highlight results and conjectures on Shimura varieties and more general locally symmetric spaces, with a view towards the Calegari-Geraghty method to prove modularity lifting theorems beyond the classical setting of Taylor-Wiles.
Cite
@article{arxiv.2311.13382,
title = {Recent progress on Langlands reciprocity for $\mathrm{GL}_n$: Shimura varieties and beyond},
author = {Ana Caraiani and Sug Woo Shin},
journal= {arXiv preprint arXiv:2311.13382},
year = {2023}
}
Comments
56 pages, to appear in the Proceedings of the 2022 IHES summer school on the Langlands program