Editing Langlands program (section)

== Objects==
The conjectures have evolved since Langlands first stated them. Langlands conjectures apply across many different groups over many different fields for which they can be stated, and each field offers several versions of the conjectures.<ref>{{citation|title=Love and Math: The Heart of Hidden Reality|first=Edward|last=Frenkel|author-link=Edward Frenkel|publisher=Basic Books|year=2013|isbn=9780465069958|page=77|url=https://books.google.com/books?id=sb0PAAAAQBAJ&pg=PT77|quote=The Langlands Program is now a vast subject. There is a large community of people working on it in different fields: number theory, harmonic analysis, geometry, representation theory, mathematical physics. Although they work with very different objects, they are all observing similar phenomena.}}</ref> Some versions{{which|date=September 2012}} are vague, or depend on objects such as [[Langlands group]]s, whose existence is unproven, or on the ''L''-group that has several non-equivalent definitions.

Objects for which Langlands conjectures can be stated:
*Representations of [[reductive group]]s over local fields (with different subcases corresponding to archimedean local fields, ''p''-adic local fields, and completions of function fields)
*Automorphic forms on reductive groups over global fields (with subcases corresponding to number fields or function fields).
*Analogues for finite fields.
*More general fields, such as function fields over the complex numbers.