Abstract：

In this series of lectures, we apply the results on Breuil-Kisin classification of p-divisible groups to construct smooth integral canonical models for Shimura varieties of Hodge type, following ^[4].  As a preliminary, we will first review the results of Deligne ^[2], Blasius ^[1] and Wintenberger about Hodge cycles on abelian varieties. Then we will cover the main results of section 2 (and some related parts of section 1) of  Kisin’s paper ^[4]. If time permits, we will also discuss some improvements due to Kim-Madapusi Pera ^[3] (for p=2) and Yujie Xu ^[5] (on the normalization process).

References: 

[1] D. Blasius, A p-adic property of Hodge classes on abelian varieties, in “Motives”, Proc. Sympos. Pure Math. 55, Part 2, Amer. Math. Soc., pp. 293-308, 1994.

[2] P. Deligne, Hodge cycles on abelian varieties, in “Hodge cycles, motives, and Shimura varieties”,  Lecture Notes in Math. 900, pp. 9-100, Springer-Verlag, 1982.

[3] W. Kim, K. Madapusi Pera, 2-adic integral canonical models, Forum Math. Sigma 4, e28, 2016.

[4] M. Kisin, Integral models for Shimura varieties of abelian type, J. Amer. Math. Soc. 23, pp. 967-1012, 2010.

[5] Y. Xu, Normalization in integral models of Shimura varieties of Hodge type, arXiv:2007.01275

Time:

 6.1, 6.2    ：13：30—15：00

 6.12         ：13：00—14：30

 6.13         ：10：00—11：30