Algebraic cycles for the Siegel sixfold and the exceptional theta lift from G2

Abstract: In this talk, we will report some progress towards the Beilinson conjectures for Shimura varieties associated to the symplectic group $\mathrm{GSp}(6)$. We will describe a cohomological formula for the residue at $s=1$ of the degree 8 spin $L$-function. We will then discuss an important family of cuspidal automorphic representations for $\mathrm{PGSp}(6)$ for which the residue is non-zero and relate this to the existence of an algebraic cycle coming from a Hilbert modular subvariety. This relation partially answers a question of Gross and Savin on motives with Galois group of type $\mathrm{G}2$. This is joint work with Francesco Lemma and Joaquin Rodrigues Jacinto.

algebraic geometrynumber theory

Audience: researchers in the topic

( paper | slides )

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Rendez-vous on special values and periods

Series comments: The main objective of this conference is to gather together young researchers interested in special values of L-functions and periods. These objects are at the crossroads of many recent important developments in arithmetic geometry, such as Euler systems or the theory of motives. The different talks will portray the variety of viewpoints with which L-functions and periods are studied at present.

Registration is free and mandatory, to get access to the livestream and recording of the talks.

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