2022 Fall POSTECH-PMI NUMBER THEORY SEMINAR

• Speaker : Maria Fox (Oklahoma State University, USA)
• Time : 2022.10.14.(Fri) 10:00 ~ 12:00
• Online Streaming(Zoom)

Title : Supersingular Loci of Unitary Shimura Varieties

Abstract : The supersingular locus of a unitary Shimura variety parametrizes supersingular abelian varieties with an action of a quadratic imaginary field, meeting a certain signature condition. In low-dimensional cases, every irreducible component of the supersingular locus is isomorphic to a Deligne-Lusztig variety, and the intersection combinatorics are governed by a Bruhat-Tits building. We'll consider these low-dimensional cases for motivation, and then see how the structure of the supersingular locus can be very different in general. (The new result in this talk is joint with Naoki Imai.)