报告题目：Reductive Semi-Stable Moduli Spaces

报告时间：2024-09-19   16:00-17:00

报  告 人 ：Prof.Lin Weng   Kyushu University Japan

报告地点：武汉大学理学院东北楼四楼报告厅

Abstract：There are rich mathematical structures and theories for the classical triple (X,X ̅^BS,X ̅^rBS) consisting of a locally symmetric space X, its Borel-Serre compactification X ̅^BS and the induced reductive Borel-Serre compactification X ̅^rBS . Motivated by these, for a split reductive group G/F over a number filed and an integral reductive extension G/O_F over the ring of integers, with respect to a fixed G-torsor E on Spec O_F , we construct a new stable triple (M_(ε,F)^s,M_(ε,F)^ss,M_(ε,F)^rss ）of stable, semi-stable and reductive semi-stable moduli spaces for arithmetic G-torsors (E,h), over (Spec O_F ) ̅ , and establish the following stable analugue of Zucker’s conjcture (in the equal rank generality) identifying the 〖L 〗^2-cohomologies on the stable moduli with the intersection cohomologies on the reductive semi-stable moduli:

H_((2))^∗ (M_(ε,F)^s,V ̅ )≅IH^∗ (M_(ε,F)^rss,V ̃ ),

based on the works of Zucker, Borel-Casselman, Looijenga, Saper-Stein, Rapoport, Goresky MacPherson and Arthur, Lafforgue and Saper.