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ENDOSCOPY AND COHOMOLOGY IN A TOWER OF CONGRUENCE MANIFOLDS FOR $U(n,1)$

Part of: Complex spaces with a group of automorphisms Automorphic functions

Published online by Cambridge University Press:  15 July 2019

SIMON MARSHALL Open the ORCID record for SIMON MARSHALL [Opens in a new window]  and
SUG WOO SHIN
SIMON MARSHALL
Affiliation:
Department of Mathematics, University of Wisconsin – Madison, 480 Lincoln Drive, Madison, WI 53706, USA; [email protected]
SUG WOO SHIN
Affiliation:
Department of Mathematics, University of California, Berkeley, 901 Evans Hall, Berkeley, CA 94720, USA; [email protected] Korea Institute for Advanced Study, Dongdaemun-gu, Seoul 130-722, Republic of Korea

Abstract

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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 expect that the growth exponents we obtain are sharp in all degrees.

MSC classification

Primary: 32N10: Automorphic forms
Secondary: 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 7 , 2019 , e19
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2019

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