Statements (57)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
|
| gptkbp:field |
gptkb:algebraic_geometry
number theory |
| gptkbp:generalizes |
gptkb:Hilbert_modular_surfaces
gptkb:modular_curves |
| gptkbp:hasProperty |
can be compact or non-compact
admit Hecke correspondences admit canonical models admit stratifications can be singular or non-singular defined over number fields have bad and good reduction have complex points with moduli interpretation have reduction modulo primes linked to Galois representations linked to Hodge theory linked to motives play role in reciprocity laws related to André-Oort conjecture related to Drinfeld modular varieties related to Ekedahl-Oort stratification related to GSpin groups related to Hodge cycles related to Kuga varieties related to L-functions related to Mumford-Tate groups related to Newton polygons related to Oort conjecture related to PEL-type moduli problems related to Satake compactification related to Sato-Tate conjecture related to Siegel modular varieties related to Zilber-Pink conjecture related to moduli of K3 surfaces related to moduli of abelian varieties related to orthogonal Shimura varieties related to p-adic Hodge theory related to special points (CM points) related to toroidal compactification related to unitary Shimura varieties used in proof of Fermat's Last Theorem used in proof of modularity theorem parameterize abelian varieties with additional structure can be described as quotients of Hermitian symmetric domains by arithmetic groups |
| https://www.w3.org/2000/01/rdf-schema#label |
Shimura varieties
|
| gptkbp:namedAfter |
gptkb:Goro_Shimura
|
| gptkbp:relatedTo |
gptkb:Langlands_program
arithmetic geometry automorphic forms moduli spaces |
| gptkbp:studiedBy |
gptkb:André_Weil
gptkb:Goro_Shimura gptkb:Pierre_Deligne |
| gptkbp:bfsParent |
gptkb:Langlands_program
gptkb:Langlands_correspondence gptkb:Algebraic_number_theory |
| gptkbp:bfsLayer |
5
|