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Jean-Steffan Koskivirta: Group-theoretical Hasse invariants

Tid: On 2017-03-01 kl 13.15 - 15.00

Plats: Room 3418, KTH

Medverkande: Jean-Steffan Koskivirta, Imperial College, London

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If A is an abelian variety over a field of characteristic p, the p-torsion of A is a finite group scheme called truncated Barsotti–Tate groups of level 1 (in short BT1). Moonen and Wedhorn understood that isomorphism classes of BT1's over a perfect field can be classified in group-theoretical terms. If A is now an abelian variety over a scheme S of characteristic p, then S is naturally stratified by the isomorphism class of the p-torsion of the fibers. For example if S is the special fiber of a Shimura variety, this is usually called the Ekedahl–Oort stratification.

The theory of F-zips and G-zips developed by Pink, Wedhorn and Ziegler introduces an algebraic stack whose points parametrize the isomorphism classes of BT1's. In a joint work with Wushi Goldring, we constructed group-theoretical Hasse invariants for the stack of G-zips. As an application, we show that the Ekedahl–Oort stratification is principally pure. In this talk, we will explain the basics of the construction of Hasse invariants, and discuss some applications.

Tillhör: Stockholms Matematikcentrum
Senast ändrad: 2017-02-23