Eisenstein classes and hyperplane complements

Abstract: In recent years several authors (Sczech, Nori, Hill, Charollois-Dasgupta-Greenberg, Beilinson-Kings-Levin) have defined and studied certain group cocycles ("Eisenstein cocycles") in the cohomology of arithmetic groups. I will discuss how these constructions can be understood in terms of equivariant cohomology and characteristic classes. This point of view relates the cocycles to the theta correspondence and leads to generalisations relating the homology of arithmetic groups to algebraic objects such as meromorphic differentials on hyperplane complements. I will discuss these generalisations and an application to critical values of L-functions.

The talk is based on joint work-in-progress with Nicolas Bergeron, Pierre Charollois and Akshay Venkatesh.

number theory

Audience: researchers in the topic

London number theory seminar

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