Supersingular Loci of Unitary (2,m-2) Shimura Varieties

Abstract: The supersingular locus of a Unitary (2,m-2) Shimura variety parametrizes supersingular abelian varieties of dimension m, with an action of a quadratic imaginary field meeting the "signature (2,m-2)" condition. In some cases, for example when m=3 or m=4, 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 cases for motivation, and then see how the structure of the supersingular locus becomes very different for m>4. (The new result in this talk is joint with Naoki Imai.)

number theory

Audience: researchers in the topic

University of Arizona Algebra and Number Theory Seminar