On higher regulators for Siegel Shimura varieties

Abstract: In this talk, we will report some progress towards the Beilinson conjectures for Shimura varieties associated to the symplectic group GSp(6). We will explain how to construct classes in its motivic cohomology and how to compute their image by Beilinson's higher regulator in terms of Rankin-Selberg type automorphic integrals. Using results of Pollack and Shah, we relate the integral to a non-critical special value of the degree 8 spin L-function. If time permits, we will describe parallel work in progress, which relates the residue at s=1 of these automorphic integrals to the existence of a Tate class coming from a Hilbert modular subvariety. This relation partially answers a question of Gross and Savin on motives with Galois group of type G2. This is joint work with Francesco Lemma and Joaquin Rodrigues Jacinto.

number theory

Audience: researchers in the topic

CRM-CICMA Québec Vermont Seminar Series

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