# Lafforgue pseudocharacters and the construction of Galois representations

`2021-01-20 10:30:00``2021-01-20 11:30:00``Lafforgue pseudocharacters and the construction of Galois representations``A key goal of the Langlands program is to attach Galois representations to automorphic representations. In general, there are two methods to construct these representations. The first, and the most effective, is to extract the Galois representation from the étale cohomology of a suitable Shimura variety. However, most Galois representations cannot be constructed in this way. The second, more general, method is to construct the Galois representation, via its corresponding pseudocharacter, as a p-adic limit of Galois representations constructed using the first method. In this talk, I will give an expository overview of the second method. I will then demonstrate how this construction can be refined by using V. Lafforgue’s G-pseudocharacters in place of classical pseudocharacters. As an application, I will prove that the Galois representations attached to certain irregular automorphic representations of U(a,b) are odd, generalising a result of Bellaïche-Chenevier in the regular case. This work is joint with Tobias Berger. ========================= Topic: BIU Algebra Seminar -- Weiss Time: Jan 20, 2021 10:30 AM Jerusalem Join Zoom Meeting https://us02web.zoom.us/j/81294386230?pwd=SFE0bXhmTGUxZzZRWlI2WE9pL3dhdz09 Meeting ID: 812 9438 6230 Passcode: 233810``Zoom -- see invitation below``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`A key goal of the Langlands program is to attach Galois representations to automorphic representations. In general, there are two methods to construct these representations. The first, and the most effective, is to extract the Galois representation from the étale cohomology of a suitable Shimura variety. However, most Galois representations cannot be constructed in this way. The second, more general, method is to construct the Galois representation, via its corresponding pseudocharacter, as a p-adic limit of Galois representations constructed using the first method.

In this talk, I will give an expository overview of the second method. I will then demonstrate how this construction can be refined by using V. Lafforgue’s G-pseudocharacters in place of classical pseudocharacters. As an application, I will prove that the Galois representations attached to certain irregular automorphic representations of U(a,b) are odd, generalising a result of Bellaïche-Chenevier in the regular case. This work is joint with Tobias Berger.

=========================

Topic: BIU Algebra Seminar -- Weiss

Time: Jan 20, 2021 10:30 AM Jerusalem

Join Zoom Meeting

https://us02web.zoom.us/j/81294386230?pwd=SFE0bXhmTGUxZzZRWlI2WE9pL3dhdz09

Meeting ID: 812 9438 6230

Passcode: 233810

Last Updated Date : 17/01/2021