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Endoscopy and Cohomology of a Quasi-Split U(4)

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Families of Automorphic Forms and the Trace Formula

Part of the book series: Simons Symposia ((SISY))

Abstract

We prove asymptotic upper bounds for the L 2 Betti numbers of the locally symmetric spaces associated with a quasi-split U(4). These manifolds are 8-dimensional, and we prove bounds in degrees 2 and 3, with the behavior in the other degrees being well understood. In degree 3, we conjecture that these bounds are sharp. Our main tool is the endoscopic classification of automorphic representations of U(N) by Mok.

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Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No. DMS-1201321 and DMS-1509331.

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin–Madison, 480 Lincoln Drive, Madison, WI, 53706, USA

    Simon Marshall

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  1. Simon Marshall
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Correspondence to Simon Marshall .

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Editors and Affiliations

  1. Mathematical Institute, University of Bonn, Bonn, Nordrhein-Westfalen, Germany

    Werner Müller

  2. Department of Mathematics, University of California, Berkeley, Berkeley, California, USA

    Sug Woo Shin

  3. Department of Mathematics, Cornell University, Ithaca, New York, USA

    Nicolas Templier

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Marshall, S. (2016). Endoscopy and Cohomology of a Quasi-Split U(4). In: Müller, W., Shin, S., Templier, N. (eds) Families of Automorphic Forms and the Trace Formula. Simons Symposia. Springer, Cham. https://doi.org/10.1007/978-3-319-41424-9_8

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