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.

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Topic: BIU Algebra Seminar -- Weiss

Time: Jan 20, 2021 10:30 AM Jerusalem

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