Abstract Judith Ludwig

Judith Ludwig will speak on

Perfectoid Harris-Taylor Shimura varieties and a quotient of the Lubin-Tate tower

Abstract: Let K/Q_p be a finite extension and consider the parabolic subgroup P(K) of GL_n(K) of block form (n-1,1). In this talk I will explain how to construct the quotient of the infinite-level Lubin-Tate space by the parabolic P(K) as a perfectoid space. For this we prove some perfectoidness results for certain Harris-Taylor Shimura varieties at infinite level. As an application of the quotient construction we show a vanishing theorem for Scholze's candidate for the mod p Jacquet-Langlands and the mod p local Langlands correspondence. This is joint work with C. Johansson.