Langlands programme

alternative Langlands program

1. mathematicsA set of interconnected, far-reaching and consequential conjectures connecting number theory with geometry.

   Quickly recognised as an imaginative vision, the so-called Langlands programme has been a bountiful source of ideas and might conceivably lead one day to a unified approach to mathematics.

   2019, Graham Farmelo, The Universe Speaks in Numbers, Faber & Faber, unnumbered page

   2 more examples

   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.

plural Langlands programmes · alternative Langlands program

1. mathematicsAny of several similar sets of conjectures applicable to restricted domains of number theory and/or geometry.

   p-adic Langlands programme

   1 more example

   modulo p Langlands programme