Simon Marshall, Sug Woo Shin
Published 2018-04-13Version 1
By assuming the endoscopic classification of automorphic representations on inner forms of unitary groups, which is currently work in progress by Kaletha, Minguez, Shin, and White, we bound the growth of cohomology in congruence towers of locally symmetric spaces associated to $U(n,1)$. In the case of lattices arising from Hermitian forms, we conjecture that the growth exponents we obtain are sharp in all degrees.
Endoscopic Classification of Representations: Inner Forms of Unitary Groups
Raising the level of automorphic representations of $\mathrm{GL}_{2n}$ of unitary type
Eisenstein series and automorphic representations
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