Abstract: In this talk I will report on joint work with Christian Johansson. The aim of our project is to construct a quotient of an infinite level Lubin-Tate space by a certain parabolic subgroup of GL(n,F) (F/Qp finite) as a perfectoid space. The motivation for constructing this quotient is as follows. As I will explain in the talk, Scholze recently constructed a candidate for the mod p Jacquet-Langlands correspondence and the mod p local Langlands correspondence for GL(n,F) . Given a smooth admissible representation π of GL(n,F) , the candidate for these correspondences is given by the etale cohomology groups of the adic projective space Pn−1 with coefficients in a sheaf Fπ that one constructs from π . The finer properties of this candidate remain mysterious. As an application of the quotient construction one can show a vanishing result for some of these cohomology groups Hiet(Pn−1,Fπ) .
As usual, the seminar will be preceded by various study groups, starting at 1200.
The talks will be preceded by tea/coffee in Imperial’s common room (room 549 Huxley) from 3:30.