Langlands programme

== English == === Alternative forms === Langlands program === Etymology === Named after Canadian mathematician Robert Langlands, who proposed it in 1967 (privately) and publicly in 1970. === Proper noun === Langlands programme (mathematics) A set of interconnected, far-reaching and consequential conjectures connecting number theory with geometry. 2009, Clifton Cunningham, Monica Nevins (editors), Ottawa Lectures on Admissible Representations of Reductive p-adic Groups, American Mathematical Society, Fields Institute for Research in Mathematical Sciences, page xii, The Langlands Programme gives the study of representations of p-adic groups context and relevance, without which it almost certainly would not have enjoyed such a rich half-century of research.As we are reminded in Chapter 4, one should never forget that the study of representations of p-adic groups is inextricably linked with harmonic analysis. The Langlands Programme gives us a beautiful illustration of this fact. 2014, Michael Francis Atiyah, Collected Works, Volume 7: 2002—2013, Oxford University Press (Oxford Science Publications), page 233, The Langlands programme is a large programme which, if completed, will give a very satisfactory answer to the question of how to extend abelian class field theory to the general case of non-abelian extensions. It is a very big programme, that in many ways has only just started, and in it a fundamental role is played by complex linear representations of the Galois groups of algebraic extensions. ==== Translations ==== === Noun === Langlands programme (plural Langlands programmes) (mathematics) Any of several similar sets of conjectures applicable to restricted domains of number theory and/or geometry. p-adic Langlands programme modulo p Langlands programme