Cycles on Shimura varieties via geometric Satake

Algebra and Number Theory Seminar
Event time: 
Tuesday, October 11, 2016 - 12:15pm to 1:15pm
LOM 205
Liang Xiao
Speaker affiliation: 
University of Connecticut
Event description: 

I will talk about a joint work with Xinwen Zhu, in which we apply (mixed characteristic) geometric Satake theory to study the basic locus of Shimura varieties with hyperspecial level structure. We show that the irreducible components of the basic locus generate under certain genericity condition all Tate classes of the cohomology of the special fibers of Shimura varieties.