Algebraic Geometry Seminar: "Propagating algebraicity via functoriality"

Speaker: Wushi Goldring, Stockholm University

Abstract: We attempt -- and almost entirely succeed -- to classify the automorphic representations of reductive groups over number fields, for which the algebraicity of the Hecke eigenvalues is reducible via Langlands functoriality to cases already known for algebro-geometric reasons. In the positive direction, we give several examples of non-holomorphic automorphic forms which are superficially similar to Maass forms, but whose algebraicity does reduce to the cohomology of Shimura varieties via either known or open cases of functoriality; in the known cases of functoriality we are also able to attach Galois representations. In the negative direction, we give a conceptual, group-theoretic explanation for why Maass forms and many other forms are not reducible to known cases via functoriality. There remains only a sliver of cases where it is still perhaps unclear whether or not reduction via functoriality is possible.

Host: Matt Kerr