Shimura varieties at level ${\Gamma }_1(p^{\infty })$ and Galois representations

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

We show that the compactly supported cohomology of certain $\mathrm{U}(n,n)$ or $\mathrm{Sp}(2n)$-Shimura varieties with ${\Gamma }_1(p^{\infty })$-level vanishes above the middle degree. The…