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An automorphic form is a well-behaved function from a topological group $G$ to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup $\Gamma \subset G$ of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups.

16 votes

Are there motives which do not, or should not, show up in the cohomology of any Shimura vari...

The question may be precised depending on what you call "show up". More precisely: Concerning the cohomology of Shimura varieties there are two points of view: intersection cohomology or ordinary co …
Laurent F.'s user avatar
26 votes

What are the local Langlands conjectures nowadays, for connected reductive groups over a $p$...

I come back to the original question. First, the title: "What are the local Langlands conjectures nowadays, for connected reductive groups over a p-adic field?" I think they are not far from being pro …
Laurent F.'s user avatar