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arXiv · 2311.13382

Recent progress on Langlands reciprocity for $\mathrm{GL}_n$: Shimura varieties and beyond

Ana Caraiani·Sug Woo Shin
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Abstract

The goal of these lecture notes is to survey progress on the global Langlands reciprocity conjecture for $\mathrm{GL}_n$ 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.

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Ana Caraiani, Sug Woo Shin. 2023-11-22. Recent progress on Langlands reciprocity for $\mathrm{GL}_n$: Shimura varieties and beyond. https://arxiv.org/abs/2311.13382

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