|Date: Wednesday, February 25, 2015
Location: 4096 East Hall (4:00 PM to 6:00 PM)
Title: Classifying lattices in a vector space over a local field
Abstract: The affine Grassmanian is a projective variety (really, an ind-variety) over a field k that parametrizes k[[t]]-lattices in a fixed k((t))-vector space, and plays a fundamental role in geometric representation theory. Xinwen Zhu recently constructed a p-adic analog of this object: he found an algebraic space over F_p that parametrizes Z_p-lattices in a fixed Q_p-vector space. Moreover, he conjectured that this space was, in fact, a projective variety. I will explain Zhu's construction and its relevance, and then give a proof of his conjecture, emphasizing the main new geometric ingredient introduced to construct the desired ample divisor: a robust notion of determinant line bundles attached to certain sheaves that are not linear over the structure sheaf via (non-flat!) descent. This talk is based on joint work in progress with Peter Scholze.
Speaker: Bhargav Bhatt
Institution: University of Michigan