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On the general linear group over arithmetic orders and corresponding cohomology groups

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Post-edited
Authors : Schwermer, Joachim (Author of the conference)
CIRM (Publisher )

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orders in central simple algebras over number fields general linear group over division algebras arithmetic groups and corresponding cohomology groups cuspidal and square-integrable cohomology construction of non-vanishing square-integrable automorphic cohomology classes digression: geometry at infinity two ingredients of the construction Jacquet-Langlands correspondence existence of cuspidal resp residual representations $GL(2_d)$ non-vanishing results
Abstract : Orders in finite-dimensional algebras over number fi give rise to interesting locally symmetric spaces and algebraic varieties. Hilbert modular varieties or arithmetically defined hyperbolic 3-manifolds, compact ones as well as noncompact ones, are familiar examples. In this talk we discuss various cases related to the general linear group $GL(2)$ over orders in division algebras defined over some number field. Geometry, arithmetic, and the theory of automorphic forms are interwoven in a most fruitful way in this work. Finally we indicate a construction of non-vanishing square-integrable cohomology classes for such arithmetically defined groups.

Keywords : arithmetic groups; cohomology of groups; automorphic forms; Hilbert modular varieties

MSC Codes :
11F55 - Groups and their modular and automorphic forms (several variables)
 11F75 - Cohomology of arithmetic groups
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 17/04/2019
    Conference Date : 27/03/2019
    Subseries : Research talks
    arXiv category : Number Theory
    Mathematical Area(s) : Number Theory
    Format : MP4 (.mp4) - HD
    Video Time : 01:02:12
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2019-03-27_Schwermer.mp4
Information on the Event

Event Title : Cohomology of arithmetic groups, lattices and number theory: geometric and computational viewpoint / Cohomologie des groupes arithmétiques, réseaux et théorie des nombres: géométries et calculs
Event Organizers : Bayer-Fluckiger, Eva ; Elbaz-Vincent, Philippe ; Ellis, Graham ; Gunnels, Paul
Dates : 25/03/2019 - 29/03/2019
Event Year : 2019
Event URL : https://conferences.cirm-math.fr/1995.html

Citation Data

DOI : 10.24350/CIRM.V.19508503
Cite this video as: Schwermer, Joachim (2019). On the general linear group over arithmetic orders and corresponding cohomology groups. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19508503
URI : http://dx.doi.org/10.24350/CIRM.V.19508503

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