Title: On the general linear group over arithmetic orders and corresponding cohomology groups
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.
Recording during the meeting "Cohomology of Arithmetic Groups, Lattices and Number Theory: Geometric and Computational Viewpoint" the March 27, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
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