Arithmetic group cohomology: coefficients and automorphy

Abstract: Cohomology of arithmetic subgroups, with coefficients being algebraic representations of the corresponding reductive group, has played an important role in the construction of Langlands correspondence. Traditionally the first step to access these objects is to view them as cohomology of (locally constant) sheaves on locally symmetric spaces and hence connect them with spaces of functions. However, sometimes infinite dimensional coefficients also naturally arise, e.g. when you try to attach elliptic curves to weight 2 eigenforms on $\mathrm{GL}_2$ / an imaginary cubic field, and the sheaf theoretic viewpoint might no longer be fruitful. In this talk we’ll explain a different but very simple understanding of the connection between arithmetic group cohomology (with finite dimensional coefficients) and function spaces, and discuss the application of this idea to infinite dimensional coefficients.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Comments: Zoom ID: 663 6110 0929

Zoom password: 059123

Link: zoom.com.cn/j/66361100929?pwd=Y2JQdTd5QnhEOFBKWVRDR1JsV1VZZz09

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POINTS - Peking Online International Number Theory Seminar

Series comments: Description: Seminar on number theory and related topics

This seminar series is sponsored by the Beijing International Center of Mathematical Research (BICMR) and the School of Mathematical Sciences of Peking University.

The conference number and password are available on the external website. See also the announcements on bicmr.pku.edu.cn

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