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Abstract: |
In this talk, we will study the arithmetic geometry of the GSpin and SO Shimura varieties, which are special examples of Shimura varieties of abelian type. Over complex numbers, these Shimura varieties are closely related to moduli of hyperkaehler manifolds. Thanks to the works of Kisin and Vasiu, we can talk about smooth reductions of these varieties at good primes. It turns out the geometry over characteristic p is much finer, in the sense that these exist some natural stratifications for the reductions. We will describe all the Newton strata. Joint work with Chao Zhang. |