Langlands conjecture

English

Alternative forms

• Langlands' conjecture

Etymology

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

Noun

Langlands conjecture (plural Langlands conjectures)

1. (mathematics) Any of the conjectures that comprise the Langlands programme.
   • 1998, Daniel Bump, Automorphic Forms and Representations, Cambridge University Press, 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.

   • 2009, Huai-Dong Cao, Shing-Tung Yau (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.

   • 2013, J. W. Cogdell, 10: Langlands Conjectures for GL_n, Joseph Bernstein, Stephen Gelbart (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

any conjecture of the Langlands programme

• French: please add this translation if you can
• German: Langlands-Vermutung f
• Italian: please add this translation if you can

Further reading

• Langlands program on Wikipedia.Wikipedia