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：Peter Scholze  (波恩大学)

题  目：The geometric Satake equivalence in mixed characteristic

时  间：2017.04.11（星期二），16:30-17:30

地  点：晨兴110（视频）

Abstract: In order to apply V. Lafforgue's ideas to the study of representations of p-adic groups, one needs a version of the geometric Satake equivalence in that setting. For the affine Grassmannian defined using the Witt vectors, this has been proven by Zhu. However, one actually needs a version for the affine Grassmannian defined using Fontaine's ring B_dR, and related results on the Beilinson-Drinfeld Grassmannian over a self-product of Spa Q_p. These objects exist as diamonds, and in particular one can make sense of the fusion product in this situation; this is a priori surprising, as it entails colliding two distinct points of Spec Z. The focus of the talk will be on the geometry of the fusion product, and an analogue of the technically crucial ULA (Universally Locally Acyclic) condition that works in this non-algebraic setting.