Statements (42)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
gptkb:algebraic_geometry
group theory algebraic groups algebraic structures group schemes |
| gptkbp:citation |
Demazure, Gabriel: Groupes algébriques
Oort: Commutative group schemes Tate: Finite flat group schemes Waterhouse: Introduction to Affine Group Schemes Milne: Algebraic Groups, Lie Groups, and their Arithmetic Subgroups |
| gptkbp:class |
classified over algebraically closed fields
|
| gptkbp:defines |
group scheme of finite type over a base scheme
|
| gptkbp:example |
group scheme of p-torsion points of an abelian variety
finite constant group scheme |
| gptkbp:field |
gptkb:algebraic_geometry
group theory |
| https://www.w3.org/2000/01/rdf-schema#label |
finite group schemes
|
| gptkbp:importantFor |
gptkb:Galois_theory
modular forms arithmetic geometry deformation theory theory of motives |
| gptkbp:notablePerson |
gptkb:Jean-Pierre_Serre
gptkb:Alexander_Grothendieck gptkb:Michel_Demazure gptkb:Pierre_Cartier |
| gptkbp:property |
can be commutative
can be connected can be local can be non-commutative can be non-reduced can be étale |
| gptkbp:relatedTo |
gptkb:group_of_people
gptkb:Lie_group group scheme |
| gptkbp:structure |
represented by finite-dimensional commutative Hopf algebras
|
| gptkbp:studiedIn |
gptkb:algebraic_geometry
|
| gptkbp:usedIn |
study of abelian varieties
study of elliptic curves |
| gptkbp:bfsParent |
gptkb:p-divisible_groups
|
| gptkbp:bfsLayer |
8
|