In mathematics, the local Langlands conjectures, introduced by Robert Langlands (1967, 1970), are part of the Langlands program. They describe a correspondence between the complex representations of a reductive algebraic group G over a local field F, and representations of the Langlands group of F into the L-group of G. This correspondence is not a bijection in general. The conjectures can be thought of as a generalization of local class field theory from abelian Galois groups to non-abelian Galois groups.
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In mathematics, the localLanglandsconjectures, introduced by Robert Langlands (1967, 1970), are part of the Langlands program. They describe a correspondence...
The Langlandsconjectures for GL(1, K) follow from (and are essentially equivalent to) class field theory. Langlands proved the Langlandsconjectures for...
Phelan Langlands, CC FRS FRSC (/ˈlæŋləndz/; born October 6, 1936) is a Canadian mathematician. He is best known as the founder of the Langlands program...
In mathematics, the geometric Langlands correspondence is a reformulation of the Langlands correspondence obtained by replacing the number fields appearing...
fields of proper regular schemes flat over integers. Higher local field LocalLanglandsconjectures Norm group Hasse, H. (1930), "Die Normenresttheorie relativ-Abelscher...
the Langlands program as a natural realm of examples for testing conjectures. In papers in 1977 and 1978, Barry Mazur proved the torsion conjecture giving...
spaces yields the solution to a special case of the weight-monodromy conjecture. Scholze and Bhargav Bhatt have developed a theory of prismatic cohomology...
the André–Oort and Griffiths conjecture 2023 Ana Caraiani – "For diverse transformative contributions to the Langlands program, and in particular for...
Poincaré conjecture), Fermat's Last Theorem, and others. Conjectures disproven through counterexample are sometimes referred to as false conjectures (cf....
contributions to the Langlands program. In 1993, he—along with Gérard Laumon and Michael Rapoport—proved the localLanglandsconjectures for the general linear...
L-functions. The Langlands dual was introduced by Langlands (1967) in a letter to A. Weil. The L-group is used heavily in the Langlandsconjectures of Robert...
modern algebraic geometry and number theory. The conjectures concern the generating functions (known as local zeta functions) derived from counting points...
Langlands–Deligne local constant Weil-Deligne group Additionally, many different conjectures in mathematics have been called the Deligne conjecture:...
generalizations of class field theory: higher class field theory, the Langlands program (or 'Langlands correspondences'), and anabelian geometry. In modern mathematical...
McQuillan in 1972. In 1980, Kutzko proved the localLanglandsconjectures for the general linear group GL2(K) over local fields. In 2014, he became a Fellow of...
prove the remaining cases of the Langlandsconjectures for GL2. Laurent Lafforgue proved the Langlandsconjectures for GLn of a function field by studying...
Fargues has formulated a general geometric conjecture which refines the classical localLanglandsconjecture, and at the same time introduces extra structure...
1007/BFb0073145, MR 0748505 Bushnell, Colin J.; Henniart, Guy (2006), The localLanglandsconjecture for GL(2), Grundlehren der Mathematischen Wissenschaften [Fundamental...
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