Langlands program for function fields

URI: https://gptkb.org/entity/Langlands_program_for_function_fields
GPTKB entity
Statements (29)
Predicate Object
gptkbp:instanceOf gptkb:logic
gptkbp:appliesTo function fields over finite fields
gptkbp:concerns modular forms
L-functions
automorphic forms
Galois representations
gptkbp:field gptkb:algebraic_geometry
number theory
gptkbp:firstMajorResultYear 1970s
https://www.w3.org/2000/01/rdf-schema#label Langlands program for function fields
gptkbp:influencedBy gptkb:Robert_Langlands
gptkbp:involves gptkb:étale_cohomology
representation theory
reductive algebraic groups
algebraic curves over finite fields
moduli spaces of shtukas
gptkbp:notableAchievement Drinfeld's proof for GL(2)
Lafforgue's proof for GL(n)
gptkbp:notablePerson gptkb:Laurent_Lafforgue
gptkb:Vladimir_Drinfeld
gptkbp:notablePublication Drinfeld, 1974
Lafforgue, 2002
gptkbp:notableWinner Fields Medal (Drinfeld, Lafforgue)
gptkbp:partOf gptkb:Langlands_program
gptkbp:relatedTo gptkb:Langlands_correspondence
gptkbp:status open for general reductive groups
proven for GL(n)
gptkbp:bfsParent gptkb:Drinfeld_module
gptkbp:bfsLayer 5