Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:hasSubfield |
number theory
representation theory automorphic forms |
| https://www.w3.org/2000/01/rdf-schema#label |
Langlands conjectures
|
| gptkbp:influenced |
gptkb:algebraic_geometry
representation theory arithmetic geometry modern number theory |
| gptkbp:notableAchievement |
proof of Fermat's Last Theorem (via modularity theorem)
proof of Langlands correspondence for GL(2) over Q proof of Sato–Tate conjecture (as a consequence) proof of local Langlands conjecture for GL(n) proof of global Langlands conjecture for function fields |
| gptkbp:proposedBy |
gptkb:Robert_Langlands
1967 |
| gptkbp:relatedTo |
gptkb:Langlands_program
modular forms L-functions Galois representations automorphic representations functoriality principle reciprocity laws |
| gptkbp:seeAlso |
gptkb:Taniyama–Shimura_conjecture
gptkb:Weil_conjectures gptkb:Langlands_dual_group gptkb:Arthur–Selberg_trace_formula |
| gptkbp:status |
open
|
| gptkbp:bfsParent |
gptkb:lion
|
| gptkbp:bfsLayer |
4
|