Langlands conjecture

English Alternative forms en Langlands' conjecture Etymology Named after Canadian mathematician Robert Langlands; interpretable as a reference to the Langlands programme. Noun en mathematics Any of the conjectures that comprise the Langlands programme. en 1998 Daniel Bump Automorphic Forms and Representations Cambridge University Press https://books.google.com.au/books?id=QQ1cr7B6XqQC&pg=PA90&dq=%22Langlands+conjectures%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjQ3MXMm9iGAxWrR2wGHaheD2EQ6AF6BAhMEAI#v=onepage&q=%22Langlands%20conjectures%22&f=false 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. en 2009 Huai-Dong Cao; Shing-Tung Yau Surveys in Differential Geometry International Press https://books.google.com.au/books?id=G1rvAAAAMAAJ&q=%22Langlands+conjecture%22%7C%22Langlands+conjectures%22&dq=%22Langlands+conjecture%22%7C%22Langlands+conjectures%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjxuZSNjtiGAxVD1TgGHVEuFXwQ6AF6BAhUEAI 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. en 2013 James Cogdell J. W. Cogdell 10: Langlands Conjectures for GLn Joseph Bernstein; Stephen Gelbart An Introduction to the Langlands Program Springer https://books.google.com.au/books?id=vLQPBwAAQBAJ&pg=PA229&dq=%22Langlands+conjectures%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjQ3MXMm9iGAxWrR2wGHaheD2EQ6AF6BAgMEAI#v=onepage&q=%22Langlands%20conjectures%22&f=false 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. Translations any conjecture of the Langlands programme French: fr German: de Langlands-Vermutung f Italian: it Further reading Langlands program