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Session S21 - Galois representations and automorphic forms

Wednesday, July 21, 18:30 ~ 19:10 UTC-3

Applying the Langlands program to the inverse Galois problem

Adrián Zenteno

Universidad Nacional Autónoma de México, México   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In the last decade, the study of the images of the Galois representations associated to regular algebraic cuspidal automorphic representations of $GL_n(\mathbb{A}_{\mathbb{Q}})$, via global Langlands correspondence, with prescribed local conditions has been an effective strategy to address the inverse Galois problem for finite groups of Lie type. In this talk we will explain how, by combining this strategy with Langlands functoriality and globalization of supercuspidal representations, we can construct residual Galois representations with controlled image and obtain new families of finite groups of type $B_m$, $C_m$ and $D_m$ arising as Galois groups over $\mathbb{Q}$.

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