Algebra and Geometry Seminar
Shimura varieties are moduli spaces of abelian varieties with extra structures. Over the decades, various mathematicians (e.g. Rapoport, Kottwitz, Rapoport-Zink etc.) have constructed nice integral models of Shimura varieties. In this talk, I will discuss some motivic aspects of integral models of abelian type constructed by Kisin (resp. 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.