Beijing Institute of Mathematical Sciences and Applications

The Langlands program posits that automorphic forms associated to a reductive group are parametrized by Galois representations valued in its dual group. Around ten years ago, Weissman-Gan-Gao proposed an extension of the Langlands program which puts covering groups (such as the metaplectic group) under the same framework. In this minicourse, I will explain how to systematically study such covering groups using étale cohomology. Among other things, I will explain an extension of V. Lafforgue’s spectral decomposition theorem to genuine cusp forms.