学术报告：Motives with Galois group of type G2 - construction of Gross and Savin revisited

中科院数学与系统科学研究院

数学研究所

学术报告会

报告人：Prof. Sug Woo Shin(University of California, Berkeley)

题  目：Motives with Galois group of type G₂ - construction of Gross and Savin revisited

时  间：2016.06.29（星期三），15:00-16:00

地  点：晨兴数学中心610室

Abstract:

Serre asked whether there exists a motive (over Q) with Galois group G₂. Put it in another way, the question is to find (a compatible family of) ell-adic Galois representations whose image has Zariski closure G₂. This has been answered affirmatively since 2010 by Dettweiler and Reiter, Khare-Larsen-Savin, Yun, and Patrikis (including generalizations to exceptional groups other than G₂). In this talk I revisit the construction of Gross-Savin (which was conditional when proposed in 1998) which aims to realize such a motive in the cohomology of a Siegel modular variety of genus 3 via exceptional theta correspondence between G₂ and PGSp_6. Then I will explain that the construction is now unconditional due to my recent work with Arno Kret on the construction of GSpin(2n+1)-valued Galois representations in the cohomology of Siegel modular varieties, closing with some open questions raised by Gross and Savin.