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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

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.