# Jean-Stefan Koskivirta: Vector bundles on the stack of G-zips

Stockholm Wednesday Zoom Seminar

**Time: **
Wed 2020-06-03 13.15 - 14.15

**Location: **
Zoom, meeting ID: 689 4480 8319

**Participating: **
Jean-Stefan Koskivirta, Tokyo

### Abstract

The stack of G-zips of Pink-Wedhorn-Ziegler is functorially attached to a reductive group G over the finite field Fp and a cocharacter of G. It is used to define the Ekedahl-Oort stratification on the mod p reduction of a Shimura variety. It encompasses geometric information about Shimura varieties in characteristic p (for example, it carries the generalized Hasse invariants constructed by Goldring-K). In this talk, we study vector bundles on this stack. In particular, we explain a dictionary between geometric properties of this stack and representation theory of reductive groups. This is work in progress with Naoki Imai.