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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 Alexander Grothendieck, Michel Raynaud and Michel Demazure in the early 1960s.".
- Group_scheme wikiPageID "510523".
- Group_scheme wikiPageLength "22150".
- Group_scheme wikiPageOutDegree "60".
- Group_scheme wikiPageRevisionID "659294050".
- Group_scheme wikiPageWikiLink Abelian_variety.
- Group_scheme wikiPageWikiLink Alexander_Grothendieck.
- Group_scheme wikiPageWikiLink Algebraic_geometry.
- Group_scheme wikiPageWikiLink Algebraic_group.
- Group_scheme wikiPageWikiLink Algebraic_torus.
- Group_scheme wikiPageWikiLink Andrew_Wiles.
- Group_scheme wikiPageWikiLink Category:Algebraic_groups.
- Group_scheme wikiPageWikiLink Category:Duality_theories.
- Group_scheme wikiPageWikiLink Category:Hopf_algebras.
- Group_scheme wikiPageWikiLink Category:Scheme_theory.
- Group_scheme wikiPageWikiLink Category_(mathematics).
- Group_scheme wikiPageWikiLink Category_of_groups.
- Group_scheme wikiPageWikiLink Change_of_rings.
- Group_scheme wikiPageWikiLink Class_field_theory.
- Group_scheme wikiPageWikiLink Coherent_sheaf.
- Group_scheme wikiPageWikiLink Deformation_theory.
- Group_scheme wikiPageWikiLink Diagonalizable_group.
- Group_scheme wikiPageWikiLink Dieudonné_module.
- Group_scheme wikiPageWikiLink Elliptic_curve.
- Group_scheme wikiPageWikiLink Formal_group.
- Group_scheme wikiPageWikiLink Fundamental_group_scheme.
- Group_scheme wikiPageWikiLink Galois_module.
- Group_scheme wikiPageWikiLink Glossary_of_arithmetic_and_Diophantine_geometry.
- Group_scheme wikiPageWikiLink Group_action.
- Group_scheme wikiPageWikiLink Group_object.
- Group_scheme wikiPageWikiLink Gérard_Laumon.
- Group_scheme wikiPageWikiLink Hopf_algebra.
- Group_scheme wikiPageWikiLink Inner_automorphism.
- Group_scheme wikiPageWikiLink John_Tate.
- Group_scheme wikiPageWikiLink Kernel_(category_theory).
- Group_scheme wikiPageWikiLink Lie_algebra.
- Group_scheme wikiPageWikiLink Mathematics.
- Group_scheme wikiPageWikiLink Michel_Demazure.
- Group_scheme wikiPageWikiLink Michel_Raynaud.
- Group_scheme wikiPageWikiLink Modularity_theorem.
- Group_scheme wikiPageWikiLink Moduli_space.
- Group_scheme wikiPageWikiLink Monodromy.
- Group_scheme wikiPageWikiLink Motive_(algebraic_geometry).
- Group_scheme wikiPageWikiLink Natural_transformation.
- Group_scheme wikiPageWikiLink Pontryagin_duality.
- Group_scheme wikiPageWikiLink Rigid_analytic_space.
- Group_scheme wikiPageWikiLink Scheme_(mathematics).
- Group_scheme wikiPageWikiLink Set_(mathematics).
- Group_scheme wikiPageWikiLink Spectrum_of_a_ring.
- Group_scheme wikiPageWikiLink Springer_Science+Business_Media.
- Group_scheme wikiPageWikiLink Supersingular_elliptic_curve.
- Group_scheme wikiPageWikiLink Weil_restriction.
- Group_scheme wikiPageWikiLink Witt_vector.
- Group_scheme wikiPageWikiLink Yoneda_lemma.
- Group_scheme wikiPageWikiLink Étale_group_scheme.
- Group_scheme wikiPageWikiLinkText "Group Schemes".
- Group_scheme wikiPageWikiLinkText "Group scheme".
- Group_scheme wikiPageWikiLinkText "Group scheme#Cartier duality".
- Group_scheme wikiPageWikiLinkText "Group_scheme#Cartier_duality".
- Group_scheme wikiPageWikiLinkText "additive group".
- Group_scheme wikiPageWikiLinkText "commutative group scheme".
- Group_scheme wikiPageWikiLinkText "flat".
- Group_scheme wikiPageWikiLinkText "group scheme".
- Group_scheme wikiPageWikiLinkText "group scheme#Cartier duality".
- Group_scheme wikiPageWikiLinkText "subgroup scheme".
- Group_scheme wikiPageUsesTemplate Template:Citation.
- Group_scheme wikiPageUsesTemplate Template:Cite_book.
- Group_scheme wikiPageUsesTemplate Template:Group_theory_sidebar.
- Group_scheme wikiPageUsesTemplate Template:Main.
- Group_scheme subject Category:Algebraic_groups.
- Group_scheme subject Category:Duality_theories.
- Group_scheme subject Category:Hopf_algebras.
- Group_scheme subject Category:Scheme_theory.
- Group_scheme hypernym Type.
- Group_scheme type Group.
- Group_scheme type Algebra.
- Group_scheme type Group.
- Group_scheme type Variety.
- 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 sameAs Q5611270.
- Group_scheme sameAs m.02j_74.
- Group_scheme sameAs Q5611270.
- Group_scheme sameAs 群概形.
- Group_scheme wasDerivedFrom Group_scheme?oldid=659294050.
- Group_scheme isPrimaryTopicOf Group_scheme.