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