Title: On the geometry of integral models of Shimura varieties
Speaker: Yujie Xu (Columbia University)
Abstract: Shimura varieties are moduli spaces of abelian varieties with extra structures. Over the decades, various mathematicians have constructed nice integral models of Shimura varieties. In this talk, I will discuss some motivic and deformation-theoretic aspects of integral models of Hodge type (or more generally abelian type). It turns out that their motivic aspects are related to the Hodge Conjecture for abelian varieties. I will talk about my work on improving the construction of these integral models, which have nice applications to abelian varieties and their cycles.
If time permits, I will sketch how to deduce a new CM (complex multiplication) lifting result, as well as various other applications to the geometry of Shimura varieties.
URL associated with Seminar: https://research.math.osu.edu/numbertheory/
