# Ludvig Modin: G-Zips and Globals Sections Cones

**Time: **
Fri 2021-08-27 10.30 - 11.30

**Location: **
Zoom, meeting ID: 695 2070 6048 (password required, contact arias@math.su.se)

**Respondent: **
Ludvig Modin

**Abstract:** The topic of this thesis is the stack of *G*-Zips and what we can say about the geometry of *G*-Zip schemes, schemes with a nice map into this stack. In particular, it treats the cone conjecture of Goldring and Koskivirta. The cone conjecture states that the global sections of certain vector bundles on a *G*-Zip scheme are determined by the global sections of a related bundle over the stack of *G*-Zips. An exposition of a basic strategy of proof is given, followed by an application of this strategy to the case where *G* is of Dynkin type \(C_2\).

We conclude with a discussion of applications to good reductions of Shimura varieties.