Statements (46)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
mathematical object
|
| gptkbp:associated_with |
gptkb:Hecke_algebras
modular forms the theory of algebraic groups. Shimura_data |
| gptkbp:can_be |
generalized abelian varieties
|
| gptkbp:context |
moduli_problems
|
| gptkbp:defines |
number fields
|
| gptkbp:designatedAs |
their associated groups
their associated Galois representations their level structures |
| gptkbp:hasPrograms |
arithmetic geometry
|
| gptkbp:hasStudentOrganizations |
complex geometry
|
| https://www.w3.org/2000/01/rdf-schema#label |
Shimura varieties
|
| gptkbp:is_a |
algebraic variety
symmetric spaces |
| gptkbp:is_designed_to |
algebraic groups
|
| gptkbp:is_essential_for |
the arithmetic of elliptic curves
|
| gptkbp:is_integrated_with |
projective spaces
Hermitian_symmetric_spaces |
| gptkbp:is_linked_to |
representation theory
|
| gptkbp:is_recognized_for |
finite fields
quotients of symmetric spaces |
| gptkbp:is_studied_in |
Galois cohomology
Galois representations L-functions automorphic representations cohomological methods the geometry of numbers arithmetic groups the arithmetic of modular forms Hodge_theory the_Langlands_correspondence |
| gptkbp:is_used_in |
number theory
p-adic L-functions p-adic representations |
| gptkbp:isConnectedTo |
gptkb:Langlands_program
the theory of motives the theory of motives and cycles moduli_spaces the_theory_of_algebraic_cycles |
| gptkbp:previousName |
gptkb:Goro_Shimura
|
| gptkbp:related_to |
automorphic forms
special values of L-functions the theory of special values of zeta functions |
| gptkbp:standardFeatures |
modular curves
|