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

Algebra and Number Theory Seminar

Supersingular Loci of Unitary (2,m-2) Shimura Varieties
Series: Algebra and Number Theory Seminar
Location: Zoom Meeting
Presenter: Maria Fox, University of Oregon

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 tthe 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.)