On normalization in the integral models of Shimura varieties of Hodge type

Abstract: Shimura varieties are moduli spaces of abelian varieties with extra structures. Over the decades, various mathematicians (e.g. Rapoport, Kottwitz, etc.) have constructed integral models of Shimura varieties. In this talk, I will discuss some motivic aspects of integral models of Hodge type constructed by Kisin (resp. Kisin-Pappas). I will talk about recent work on removing the normalization step in the construction of such integral models, which gives closed embeddings of Hodge type integral models into Siegel integral models under some assumption. I will explain how this question is related to the Grothendieck Standard Conjecture D for abelian varieties, and sketch a proof of this type of questions if time permits. I will also mention an application to toroidal compactifications of Hodge type integral models.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Columbia Automorphic Forms and Arithmetic Seminar