Langlands conjecture
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English
[edit]Alternative forms
[edit]Etymology
[edit]Named after Canadian mathematician Robert Langlands; interpretable as a reference to the Langlands programme.
Noun
[edit]Langlands conjecture (plural Langlands conjectures)
- (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 GLn, 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 -dimensional representations of and the automorphic representations of which preserves these analytic invariants.
- 1998, Daniel Bump, Automorphic Forms and Representations, Cambridge University Press, page 90,
Translations
[edit]any conjecture of the Langlands programme
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Further reading
[edit]- Langlands program on Wikipedia.Wikipedia