Statements (52)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:logic
|
| gptkbp:field |
gptkb:algebraic_geometry
gptkb:mathematics number theory representation theory |
| gptkbp:generalizes |
geometric Langlands correspondence
|
| gptkbp:hasConjecture |
gptkb:Langlands_program
|
| https://www.w3.org/2000/01/rdf-schema#label |
Langlands correspondence
|
| gptkbp:influenced |
arithmetic geometry
modern number theory theory of motives |
| gptkbp:notableAchievement |
global Langlands correspondence
local Langlands correspondence proof for GL(1) is class field theory proof for GL(2) over Q by Andrew Wiles proof for function fields by Laurent Lafforgue proof for GL(n) over function fields by Laurent Lafforgue |
| gptkbp:partOf |
gptkb:Langlands_program
|
| gptkbp:proposedBy |
gptkb:Robert_Langlands
1967 |
| gptkbp:relatedTo |
gptkb:Taniyama–Shimura_conjecture
gptkb:Eisenstein_series gptkb:modular_curves gptkb:Langlands_dual_group gptkb:motivic_L-functions gptkb:Arthur–Selberg_trace_formula gptkb:Shimura_varieties gptkb:modularity_theorem gptkb:Galois_groups gptkb:Langlands_functoriality_conjecture gptkb:Sato–Tate_conjecture gptkb:automorphic_L-functions gptkb:reciprocity_conjecture Hecke algebras modular forms L-functions automorphic forms Galois representations automorphic representations trace formula adelic groups automorphic representations of reductive groups cuspidal representations functoriality principle harmonic analysis on Lie groups non-abelian class field theory parabolic subgroups reciprocity laws reciprocity map representation theory of p-adic groups |
| gptkbp:bfsParent |
gptkb:Robert_Langlands
|
| gptkbp:bfsLayer |
4
|