Till innehåll på sidan

Simon Cooper: Tautological rings of Shimura varieties

Tid: Ti 2022-11-08 kl 10.00

Plats: Cramér room, Albano building 1 and Zoom

Videolänk: Meeting ID: 627 5758 4676, Passcode: 652172

Licentiand: Simon Cooper

Granskare: Torsten Wedhorn (Technische Universität Darmstadt)

Huvudhandledare: Wushi Goldring

Exportera till kalender

Abstract

This licentiate thesis consists of two papers. In paper I the tautological ring of a Hilbert modular variety at an unramified prime is computed. The method of van der Geer in the case of $A_{g}$ is extended to deal with the case of the Hilbert modular variety, which is more complicated. An example involving the unitary group is given which shows that this method cannot be used to compute the tautological rings of all Shimura varieties of Hodge type. In paper II we compute the pushforward map from a sub flag variety defined by a Levi subgroup to the Siegel flag variety. Specifically, this is the Levi factor of the parabolic associated with the maximal rational boundary component of the Siegel Shimura datum. The method involves an explicit understanding of the pullback map and an application of the self intersection formula.