Normalization in the integral models of Shimura varieties of abelian type

Abstract: Shimura varieties are moduli spaces of abelian varieties with extra structures. Many interesting questions about abelian varieties have been answered by studying the geometry of Shimura varieties.

In order to study the mod $p$ points of Shimura varieties, over the decades, various mathematicians (e.g. Rapoport, Kottwitz, etc.) have constructed nice integral models of Shimura varieties. In this talk, I will discuss some motivic aspects of integral models of Hodge type (or more generally abelian type) constructed by Kisin and Kisin-Pappas. I will talk about my 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. I will also mention an application to toroidal compactifications of such integral models. Such results (and their proof techniques) have found interesting applications to the Kudla program (and various other programs!).

If time permits, I will also mention a new result on connected components of affine Deligne–Lusztig varieties, which gives us a new CM lifting result for integral models of Shimura varieties at parahoric levels and serves as an ingredient for my main theorem at parahoric levels.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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