Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Grothendieck_topology> ?p ?o }
- Grothendieck_topology abstract "In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space. A category together with a choice of Grothendieck topology is called a site.Grothendieck topologies axiomatize the notion of an open cover. Using the notion of covering provided by a Grothendieck topology, it becomes possible to define sheaves on a category and their cohomology. This was first done in algebraic geometry and algebraic number theory by Alexander Grothendieck to define the étale cohomology of a scheme. It has been used to define other cohomology theories since then, such as l-adic cohomology, flat cohomology, and crystalline cohomology. While Grothendieck topologies are most often used to define cohomology theories, they have found other applications as well, such as to John Tate's theory of rigid analytic geometry.There is a natural way to associate a site to an ordinary topological space, and Grothendieck's theory is loosely regarded as a generalization of classical topology. Under meager point-set hypotheses, namely sobriety, this is completely accurate—it is possible to recover a sober space from its associated site. However simple examples such as the indiscrete topological space show that not all topological spaces can be expressed using Grothendieck topologies. Conversely, there are Grothendieck topologies which do not come from topological spaces.".
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- Grothendieck_topology wikiPageWikiLink Abelian_group.
- Grothendieck_topology wikiPageWikiLink Alexander_Grothendieck.
- Grothendieck_topology wikiPageWikiLink Alexandre_Grothendieck.
- Grothendieck_topology wikiPageWikiLink Algebraic_geometry.
- Grothendieck_topology wikiPageWikiLink Algebraic_number_theory.
- Grothendieck_topology wikiPageWikiLink Algebraic_variety.
- Grothendieck_topology wikiPageWikiLink Analytic_geometry.
- Grothendieck_topology wikiPageWikiLink André_Weil.
- Grothendieck_topology wikiPageWikiLink Category:Sheaf_theory.
- Grothendieck_topology wikiPageWikiLink Category:Topos_theory.
- Grothendieck_topology wikiPageWikiLink Category_theory.
- Grothendieck_topology wikiPageWikiLink Cohomology.
- Grothendieck_topology wikiPageWikiLink Comma_category.
- Grothendieck_topology wikiPageWikiLink Contravariant_functor.
- Grothendieck_topology wikiPageWikiLink Cover_(topology).
- Grothendieck_topology wikiPageWikiLink Crystalline_cohomology.
- Grothendieck_topology wikiPageWikiLink Descent_(category_theory).
- Grothendieck_topology wikiPageWikiLink Descent_(mathematics).
- Grothendieck_topology wikiPageWikiLink Divided_power_structure.
- Grothendieck_topology wikiPageWikiLink Equaliser_(mathematics).
- Grothendieck_topology wikiPageWikiLink Equalizer_(mathematics).
- Grothendieck_topology wikiPageWikiLink Fibered_category.
- Grothendieck_topology wikiPageWikiLink Fibered_product.
- Grothendieck_topology wikiPageWikiLink Fibred_category.
- Grothendieck_topology wikiPageWikiLink Flat_cohomology.
- Grothendieck_topology wikiPageWikiLink Flat_topology.
- Grothendieck_topology wikiPageWikiLink Functor.
- Grothendieck_topology wikiPageWikiLink Fundamental_group.
- Grothendieck_topology wikiPageWikiLink Geometric_morphism.
- Grothendieck_topology wikiPageWikiLink Glossary_of_algebraic_geometry.
- Grothendieck_topology wikiPageWikiLink Gluing_axiom.
- Grothendieck_topology wikiPageWikiLink Indiscrete_topology.
- Grothendieck_topology wikiPageWikiLink Jean-Louis_Verdier.
- Grothendieck_topology wikiPageWikiLink Jean-Pierre_Serre.
- Grothendieck_topology wikiPageWikiLink Jean_Giraud_(mathematician).
- Grothendieck_topology wikiPageWikiLink John_Tate.
- Grothendieck_topology wikiPageWikiLink L-adic_cohomology.
- Grothendieck_topology wikiPageWikiLink Manifold.
- Grothendieck_topology wikiPageWikiLink Mathematics.
- Grothendieck_topology wikiPageWikiLink Module_(mathematics).
- Grothendieck_topology wikiPageWikiLink Open_cover.
- Grothendieck_topology wikiPageWikiLink Open_immersion.
- Grothendieck_topology wikiPageWikiLink Open_set.
- Grothendieck_topology wikiPageWikiLink Presheaf_(category_theory).
- Grothendieck_topology wikiPageWikiLink Princeton_University_Press.
- Grothendieck_topology wikiPageWikiLink Pullback.
- Grothendieck_topology wikiPageWikiLink Pullback_(category_theory).
- Grothendieck_topology wikiPageWikiLink Reduced_(ring_theory).
- Grothendieck_topology wikiPageWikiLink Reduced_ring.
- Grothendieck_topology wikiPageWikiLink Rigid_analytic_geometry.
- Grothendieck_topology wikiPageWikiLink Rigid_analytic_space.
- Grothendieck_topology wikiPageWikiLink Ring_(mathematics).
- Grothendieck_topology wikiPageWikiLink Scheme_(mathematics).
- Grothendieck_topology wikiPageWikiLink Sheaf_(mathematics).
- Grothendieck_topology wikiPageWikiLink Sieve_(category_theory).
- Grothendieck_topology wikiPageWikiLink Sober_space.
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- Grothendieck_topology wikiPageWikiLink Subfunctor.
- Grothendieck_topology wikiPageWikiLink Topological_space.
- Grothendieck_topology wikiPageWikiLink Topos.
- Grothendieck_topology wikiPageWikiLink Trivial_topology.
- Grothendieck_topology wikiPageWikiLink Weil_conjectures.
- Grothendieck_topology wikiPageWikiLink Yoneda_embedding.
- Grothendieck_topology wikiPageWikiLink Yoneda_lemma.
- Grothendieck_topology wikiPageWikiLink Zariski_topology.
- Grothendieck_topology wikiPageWikiLink Étale_cohomology.
- Grothendieck_topology wikiPageWikiLink Étale_map.
- Grothendieck_topology wikiPageWikiLink Étale_morphism.
- Grothendieck_topology wikiPageWikiLink Étale_topology.
- Grothendieck_topology wikiPageWikiLinkText "Grothendieck site".
- Grothendieck_topology wikiPageWikiLinkText "Grothendieck topologies".
- Grothendieck_topology wikiPageWikiLinkText "Grothendieck topology".
- Grothendieck_topology wikiPageWikiLinkText "Grothendieck topology#Alternative axioms".
- Grothendieck_topology wikiPageWikiLinkText "Grothendieck topology#The big and small étale sites".
- Grothendieck_topology wikiPageWikiLinkText "site".
- Grothendieck_topology wikiPageWikiLinkText "sites".
- Grothendieck_topology wikiPageWikiLinkText "subcanonical".
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- Grothendieck_topology subject Category:Sheaf_theory.
- Grothendieck_topology subject Category:Topos_theory.
- Grothendieck_topology hypernym Structure.
- Grothendieck_topology type Article.
- Grothendieck_topology type Building.
- Grothendieck_topology type Article.
- Grothendieck_topology type Thing.
- Grothendieck_topology comment "In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space. A category together with a choice of Grothendieck topology is called a site.Grothendieck topologies axiomatize the notion of an open cover. Using the notion of covering provided by a Grothendieck topology, it becomes possible to define sheaves on a category and their cohomology.".
- Grothendieck_topology label "Grothendieck topology".
- Grothendieck_topology seeAlso List_of_topologies_on_the_category_of_schemes.