中科院数学与系统科学研究院
数学研究所
学术报告会
报告人: Qijun Yan (Universiteit Leiden & Università degli Studi di Milano)
题 目:G-adapted deformations and Ekedahl-Oort stratification of Shimura varieties
时 间:2017.01.03(星期二),14:00-15:00
地 点:数学院南楼N818室
Abstract:
Ekedahl-Oort stratification was firstly defined and studied by Oort for the moduli space $ \mathcal{A}_{g, \mathbb{F}_p} $ of principally polarized abelian varieties over $ \mathbb{F}_p $. This notion has been generalized and studied by Moonen, Wedhorn, Viehmann and Zhang for good reduction of general Shimura varieties of Hodge type. Let $ W $ be the Weyl group of the reductive group $ G $ of a mod $ p $ Shimura variety $ S $. Then the Ekedahl-Oort strata of $ S $ are parametrized by a certain subset $ {}^JW $ of $ W $. In one of the recent works of Viehmann, it is showed that $ {}^JW $ corresponds naturally to some objects coming from the loop group $ \mathcal{L}G $ of $ G $. But this correspondence is purely group theoretic and hence one naturally asks the question: is it possible to give a direct connection between $ S $ and $ \mathcal{L}G $ (the latter is an important object from both the geometric and the arithmetic points of views)? In this talk I will explain that this connection is indeed possible. To give the connection we use the classification result of $ p $-divisible groups in term of Breuil-Kisin modules (equivalently Breuil-Kisin windows) and $ G $-adapted deformations (a notion we borrow from Kisin).