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 indvariety) 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 padic analog of this object: he found an algebraic space over F_p that parametrizes Z_plattices in a fixed Q_pvector 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 (nonflat!) descent. This talk is based on joint work in progress with Peter Scholze.
Files:
Speaker: Bhargav Bhatt
Institution: University of Michigan
Event Organizer:
