Forschungsseminar Arithmetische Geometrie

The seminar takes place either on campus, in 02.04.011, or via zoom:, please send me an email to ask for the passcode if you would like to attend.

The talks are on Wednesdays, 14:15-15:45, some might also be on Wednesday, 8-10am.

List of talks

Date Speaker Title Comments
27.10.2021 Dimitri Dine Descent theory and analytic geometry 1 2-4 pm, on campus
3.11.2021 Dimitri Dine Descent theory and analytic geometry 2 2-4 pm, on campus
9.11.2021 Paul Hamacher

The geometry and cohomology of Newton strata in Shimura varieties (Habilitationskolloquium)

Tuesday, 4:15-5:45, please ask for the zoom room if you are interested

17.11.2021 Xuhua He (Hongkong) Generic Newton points and Demazure product of Iwahori-Weyl groups via zoom, 2-4 pm
24.11.2021 Felix Schremmer Affine Bruhat order and generic Newton points 2-4 pm, on campus

Wushi Goldring


Which geometric properties of zip-schemes are generated by groups?

Abstract: Building on the theory of G-Zips developed by Pink-Wedhorn-Ziegler (generalizing earlier work by Moonen, Wedhorn, Viehmann), we study the following special case of the very general question "How much of geometry is generated by groups?": Given a scheme X in characteristic p, a connected, reductive F_p-group G, a cocharacter \mu (over an algebraic closure) and a morphism \zeta:X-->G-Zip^{\mu} we are interested in understanding how much of the geometry of X is detected by group theoretic-properties of the pair (G,\mu) and properties of the morphism \zeta (e.g. smoothness). A key example of X's which admit smooth morphisms \zeta is given by the special fibers of integral canonical models of Hodge-type Shimura varieties at a good prime p with hyperspecial level at p. Whether or not X is related to a Shimura variety, it inherits from G-Zip^{\mu} automorphic vector bundles parameterized by certain dominant weights.

We will describe theorems and conjectures about how the following geometric properties of automorphic bundles on X are controlled by (G,\mu) and zeta: (1) The cone of automorphic bundles which admit a nonzero global section, (2) The positivity (e.g. nefness, ampleness) and corresponding cohomological vanishing properties of automorphic bundles.

Based on a series of joint works with J.-S. Koskivirta and a joint work with Y. Brunebarbe, J.-S. Koskivirta and B. Stroh.

via zoom
8.12.2021 Linus Hamann (Princeton) Compatibility of the Fargues-Scholze and Gan-Takeda local Langlands Correspondence via zoom
15.12.2021 Maria Fox (Oregon) Supersingular Loci of Signature (2,m-2) Unitary Shimura Varieties via zoom