Algebraic and Arithmetic Geometry @ Bielefeld
BIREP header picture 1
 

The Bielefeld Algebraic and Arithmetic Geometry Seminar SoSe21

Welcome to the website of the Bielefeld Algebraic and Arithmetic Geometry Seminar! For more information, please contact one of the organizers: Claudia Alfes-Neumann, Eike Lau, Michael Spiess, Jeanine Van Order, Charles Vial, Thomas Zink, and also (from the Paderborn branch of the team) Fabian Januszewski.

Talks

Friday

16 July, 2021

10:30 ZiF Lennart Gehrmann (Essen)
Plectic Stark-Heegner points

Friday

16 July, 2021

11:45 ZiF Benjamin Schmidt (Hannover)
A curious moduli space on cubic threefolds

Friday

16 July, 2021

14:00 ZiF Daniel Gulotta (MPIM-Bonn)
Vanishing theorems for Shimura varieties at unipotent level and Galois representations
[Abstract]

The Langlands correspondence relates automorphic forms and Galois representations --- for example, the modular form η(z)^2 η(11z)^2 and the Tate module of the elliptic curve y^2 + y = x^3 - x^2 - 10x - 20 are related in the sense that they have the same L-function. The p-adic Langlands program aims to interpolate the Langlands correspondence in p-adic families. In this setting, the role of automorphic forms is played by the completed cohomology groups defined by Emerton.

Calegari and Emerton have conjectured that the completed cohomology vanishes above a certain degree, often denoted q_0. In the case of Shimura varieties of Hodge type, Scholze has proved the conjecture for compactly supported completed cohomology. We give a strengthening of Scholze's result under the additional assumption that the group becomes split over Q_p. More specifically, we show that the compactly supported cohomology vanishes not just at full infinite level at p, but also at unipotent level at p.

We also give an application of the above result to Galois representations. For any totally real or CM field F, Scholze has constructed Galois representations associated with torsion classes in the cohomology of locally symmetric spaces for GL_n(F). We show that, if F splits completely at the relevant prime, then the nilpotent ideal appearing in the construction can be eliminated.

This talk is based on joint work with Ana Caraiani and Christian Johansson and on joint work with Ana Caraiani, Chi-Yun Hsu, Christian Johansson, Lucia Mocz, Emanuel Reinecke, and Sheng-Chi Shih.

Friday

16 July, 2021

15:45 ZiF Ben Heuer (Bonn)
Vector bundles in the pro-étale site and non-abelian p-adic Hodge theory