Langlands conjecture

Etymology
Named after Canadian mathematician ; interpretable as a reference to the Langlands programme.

Noun

 * 1)  Any of the conjectures that comprise the Langlands programme.
 * 2) * 1998,, Automorphic Forms and Representations, , page 90,
 * It[the Langlands functoriality conjecture] is closely related to the local Langlands conjectures, which amount to a (conjectural) classification of the representations of reductive groups over local fields.
 * 1) * 2009,, (editors), Surveys in Differential Geometry, International Press, page 86,
 * This abelian case of the Geometric Langlands Conjecture amounts to the well known result that any rank of one local system (or: line bundle with flat connection) on the curve C extends uniquely to J, and this extension is natural with respect to the Abel-Jacobi map.
 * 1) * 2013,, 10: Langlands Conjectures for GLn, , (editors), An Introduction to the Langlands Program, Springer, page 229,
 * The Langlands conjectures predict the existence of a correspondence between the $$n$$-dimensional representations of $$\mathcal{G}_k$$ and the automorphic representations of $$\mathrm{GL}_n(\mathbb{A})$$ which preserves these analytic invariants.

Translations

 * French:
 * German: Langlands-Vermutung
 * Italian: