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- Group_scheme abstract "In mathematics, a group scheme is a type of algebro-geometric object equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, smooth, or defined over a field. This extra generality allows one to study richer infinitesimal structures, and this can help one to understand and answer questions of arithmetic significance. The category of group schemes is somewhat better behaved than that of group varieties, since all homomorphisms have kernels, and there is a well-behaved deformation theory. Group schemes that are not algebraic groups play a significant role in arithmetic geometry and algebraic topology, since they come up in contexts of Galois representations and moduli problems. The initial development of the theory of group schemes was due to Alexandre Grothendieck, Michel Raynaud and Michel Demazure in the early 1960s.".
- Group_scheme wikiPageID "510523".
- Group_scheme wikiPageRevisionID "601933997".
- Group_scheme hasPhotoCollection Group_scheme.
- Group_scheme subject Category:Algebraic_groups.
- Group_scheme subject Category:Hopf_algebras.
- Group_scheme subject Category:Scheme_theory.
- Group_scheme type Abstraction100002137.
- Group_scheme type Algebra106012726.
- Group_scheme type AlgebraicGroups.
- Group_scheme type Cognition100023271.
- Group_scheme type Content105809192.
- Group_scheme type Discipline105996646.
- Group_scheme type Group100031264.
- Group_scheme type HopfAlgebras.
- Group_scheme type KnowledgeDomain105999266.
- Group_scheme type Mathematics106000644.
- Group_scheme type PsychologicalFeature100023100.
- Group_scheme type PureMathematics106003682.
- Group_scheme type Science105999797.
- Group_scheme comment "In mathematics, a group scheme is a type of algebro-geometric object equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, smooth, or defined over a field.".
- Group_scheme label "Group scheme".
- Group_scheme label "群概形".
- Group_scheme sameAs m.02j_74.
- Group_scheme sameAs Q5611270.
- Group_scheme sameAs Q5611270.
- Group_scheme sameAs Group_scheme.
- Group_scheme wasDerivedFrom Group_scheme?oldid=601933997.
- Group_scheme isPrimaryTopicOf Group_scheme.