A. Caraiani

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math.NT2023

Recent progress on Langlands reciprocity for $GL_{n}$ : Shimura varieties and beyond

Ana Caraiani, Sug Woo Shin

The goal of these lecture notes is to survey progress on the global Langlands reciprocity conjecture for $GL_{n}$ over number fields from the last decade and a half. We high…

math.NT2018

Shimura varieties at level $Γ_{1} (p^{\infty})$ and Galois representations

Ana Caraiani, Daniel R. Gulotta, Chi-Yun Hsu +4

We show that the compactly supported cohomology of certain $U (n, n)$ or $Sp (2 n)$ -Shimura varieties with $Γ_{1} (p^{\infty})$ -level vanishes above the middle degree. The…

Recent progress on Langlands reciprocity for GLn​: Shimura varieties and beyond

Shimura varieties at level Γ1​(p∞) and Galois representations

Recent progress on Langlands reciprocity for $GL_{n}$ : Shimura varieties and beyond

Shimura varieties at level $Γ_{1} (p^{\infty})$ and Galois representations