Meaning of Langlands conjecture | Babel Free

Definitions

Any of the conjectures that comprise the Langlands programme.

Equivalents

Examples

“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.”

“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.”

“The Langlands conjectures predict⟳ the existence of a correspondence between the n-dimensional representations of #92;mathcal#123;G#125;#95;k and the automorphic representations of #92;mathrm#123;GL#125;#95;n(#92;mathbb#123;A#125;) which preserves these analytic invariants.”

CEFR level