Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Scheme_(mathematics)> ?p ?o }
- Scheme_(mathematics) abstract "In mathematics, schemes connect the fields of algebraic geometry, commutative algebra and number theory. Schemes were introduced by Alexander Grothendieck in 1960 in his treatise Éléments de géométrie algébrique, with the aim of developing the formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne). Schemes enlarge the notion of algebraic variety to include nilpotent elements (the equations x = 0 and x2 = 0 define the same points, but different schemes), and "varieties" defined over any commutative ring.To be technically precise, a scheme is a topological space together with commutative rings for all of its open sets, which arises from gluing together spectra (spaces of prime ideals) of commutative rings along their open subsets. In other words, it is a locally ringed space which is locally a spectrum of a commutative ring. There are many ways one can qualify a scheme. According to a basic idea of Grothendieck, conditions should be applied to a morphism of schemes. Any scheme S has a unique morphism to Spec(Z), so this attitude, part of the relative point of view, doesn't lose anything. For details on the development of scheme theory, which quickly becomes technically demanding, see first glossary of scheme theory.".
- Scheme_(mathematics) wikiPageExternalLink Grothendieck.html.
- Scheme_(mathematics) wikiPageID "364754".
- Scheme_(mathematics) wikiPageLength "12704".
- Scheme_(mathematics) wikiPageOutDegree "106".
- Scheme_(mathematics) wikiPageRevisionID "680082915".
- Scheme_(mathematics) wikiPageWikiLink Abelian_category.
- Scheme_(mathematics) wikiPageWikiLink Adjoint_functor.
- Scheme_(mathematics) wikiPageWikiLink Adjoint_functors.
- Scheme_(mathematics) wikiPageWikiLink Affine_scheme.
- Scheme_(mathematics) wikiPageWikiLink Alexander_Grothendieck.
- Scheme_(mathematics) wikiPageWikiLink Algebraic_Geometry_(book).
- Scheme_(mathematics) wikiPageWikiLink Algebraic_geometry.
- Scheme_(mathematics) wikiPageWikiLink Algebraic_space.
- Scheme_(mathematics) wikiPageWikiLink Algebraic_stack.
- Scheme_(mathematics) wikiPageWikiLink Algebraic_varieties.
- Scheme_(mathematics) wikiPageWikiLink Algebraic_variety.
- Scheme_(mathematics) wikiPageWikiLink Algebraically_closed.
- Scheme_(mathematics) wikiPageWikiLink Algebraically_closed_field.
- Scheme_(mathematics) wikiPageWikiLink André_Martineau.
- Scheme_(mathematics) wikiPageWikiLink André_Weil.
- Scheme_(mathematics) wikiPageWikiLink Birational_geometry.
- Scheme_(mathematics) wikiPageWikiLink Category:Scheme_theory.
- Scheme_(mathematics) wikiPageWikiLink Category_of_rings.
- Scheme_(mathematics) wikiPageWikiLink Category_theory.
- Scheme_(mathematics) wikiPageWikiLink Claude_Chevalley.
- Scheme_(mathematics) wikiPageWikiLink Coherent_sheaf.
- Scheme_(mathematics) wikiPageWikiLink Commutative_algebra.
- Scheme_(mathematics) wikiPageWikiLink Commutative_ring.
- Scheme_(mathematics) wikiPageWikiLink David_Eisenbud.
- Scheme_(mathematics) wikiPageWikiLink David_Mumford.
- Scheme_(mathematics) wikiPageWikiLink Derived_algebraic_geometry.
- Scheme_(mathematics) wikiPageWikiLink Direct_limit.
- Scheme_(mathematics) wikiPageWikiLink Emmy_Noether.
- Scheme_(mathematics) wikiPageWikiLink Fibre_product.
- Scheme_(mathematics) wikiPageWikiLink Final_object.
- Scheme_(mathematics) wikiPageWikiLink Finite_field.
- Scheme_(mathematics) wikiPageWikiLink Generic_point.
- Scheme_(mathematics) wikiPageWikiLink Glossary_of_algebraic_geometry.
- Scheme_(mathematics) wikiPageWikiLink Glossary_of_scheme_theory.
- Scheme_(mathematics) wikiPageWikiLink Grothendieck.
- Scheme_(mathematics) wikiPageWikiLink Grothendiecks_relative_point_of_view.
- Scheme_(mathematics) wikiPageWikiLink Group_scheme.
- Scheme_(mathematics) wikiPageWikiLink Higher_algebraic_stack.
- Scheme_(mathematics) wikiPageWikiLink Homotopy.
- Scheme_(mathematics) wikiPageWikiLink Homotopy_theory.
- Scheme_(mathematics) wikiPageWikiLink Initial_and_terminal_objects.
- Scheme_(mathematics) wikiPageWikiLink Initial_object.
- Scheme_(mathematics) wikiPageWikiLink Integer.
- Scheme_(mathematics) wikiPageWikiLink Invertible_sheaf.
- Scheme_(mathematics) wikiPageWikiLink Italian_school_of_algebraic_geometry.
- Scheme_(mathematics) wikiPageWikiLink Jacobian_variety.
- Scheme_(mathematics) wikiPageWikiLink Jean-Pierre_Serre.
- Scheme_(mathematics) wikiPageWikiLink Limit_(category_theory).
- Scheme_(mathematics) wikiPageWikiLink Locale_theory.
- Scheme_(mathematics) wikiPageWikiLink Locally_ringed_space.
- Scheme_(mathematics) wikiPageWikiLink Masayoshi_Nagata.
- Scheme_(mathematics) wikiPageWikiLink Mathematics.
- Scheme_(mathematics) wikiPageWikiLink Maximal_ideal.
- Scheme_(mathematics) wikiPageWikiLink Michael_Artin.
- Scheme_(mathematics) wikiPageWikiLink Module_(mathematics).
- Scheme_(mathematics) wikiPageWikiLink Moduli_problem.
- Scheme_(mathematics) wikiPageWikiLink Moduli_space.
- Scheme_(mathematics) wikiPageWikiLink Morphism_of_algebraic_varieties.
- Scheme_(mathematics) wikiPageWikiLink Nilpotent.
- Scheme_(mathematics) wikiPageWikiLink Number_theory.
- Scheme_(mathematics) wikiPageWikiLink Oscar_Zariski.
- Scheme_(mathematics) wikiPageWikiLink Oxford_University_Press.
- Scheme_(mathematics) wikiPageWikiLink Picard_group.
- Scheme_(mathematics) wikiPageWikiLink Pierre_Cartier_(mathematician).
- Scheme_(mathematics) wikiPageWikiLink Pierre_Deligne.
- Scheme_(mathematics) wikiPageWikiLink Pointless_topology.
- Scheme_(mathematics) wikiPageWikiLink Prime_ideal.
- Scheme_(mathematics) wikiPageWikiLink Product_(category_theory).
- Scheme_(mathematics) wikiPageWikiLink Product_topology.
- Scheme_(mathematics) wikiPageWikiLink Projective_space.
- Scheme_(mathematics) wikiPageWikiLink Projective_variety.
- Scheme_(mathematics) wikiPageWikiLink Pullback_(category_theory).
- Scheme_(mathematics) wikiPageWikiLink Regular_function.
- Scheme_(mathematics) wikiPageWikiLink Relative_scheme.
- Scheme_(mathematics) wikiPageWikiLink Ringed_space.
- Scheme_(mathematics) wikiPageWikiLink Robin_Hartshorne.
- Scheme_(mathematics) wikiPageWikiLink Separated_scheme.
- Scheme_(mathematics) wikiPageWikiLink Sheaf_(mathematics).
- Scheme_(mathematics) wikiPageWikiLink Sheaf_of_modules.
- Scheme_(mathematics) wikiPageWikiLink Spectrum_of_a_ring.
- Scheme_(mathematics) wikiPageWikiLink Springer_Science+Business_Media.
- Scheme_(mathematics) wikiPageWikiLink Stack_(mathematics).
- Scheme_(mathematics) wikiPageWikiLink Topological_space.
- Scheme_(mathematics) wikiPageWikiLink Topos.
- Scheme_(mathematics) wikiPageWikiLink Total_quotient_ring.
- Scheme_(mathematics) wikiPageWikiLink Total_ring_of_fractions.
- Scheme_(mathematics) wikiPageWikiLink Valuation_ring.
- Scheme_(mathematics) wikiPageWikiLink Weil_conjectures.
- Scheme_(mathematics) wikiPageWikiLink Wolfgang_Krull.
- Scheme_(mathematics) wikiPageWikiLink Zariski_topology.
- Scheme_(mathematics) wikiPageWikiLink Zariski–Riemann_space.
- Scheme_(mathematics) wikiPageWikiLink Éléments_de_géométrie_algébrique.
- Scheme_(mathematics) wikiPageWikiLink Étale_cohomology.
- Scheme_(mathematics) wikiPageWikiLinkText "Grothendieck's schemes".