Lecture----数学院晨兴数学中心

Title:	Motives with Galois group of type G_2 - construction of Gross and Savin revisited
Speaker:	Sug Woo Shin (University of California, Berkeley)
Time:	2016-6-29, 15:00--16:00
Place:	610
Abstract:	Serre asked whether there exists a motive (over Q) with Galois group G_2. Put it in another way, the question is to find (a compatible family of) ell-adic Galois representations whose image has Zariski closure G_2. This has been answered affirmatively since 2010 by Dettweiler and Reiter, Khare-Larsen-Savin, Yun, and Patrikis (including generalizations to exceptional groups other than G_2). 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 G_2 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.
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