Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Grothendieck_topology> ?p ?o. }
Showing items 1 to 22 of
22
with 100 items per page.
- 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.".
- Grothendieck_topology wikiPageExternalLink ~nisnevic.
- Grothendieck_topology wikiPageID "12910".
- Grothendieck_topology wikiPageRevisionID "604214114".
- Grothendieck_topology hasPhotoCollection Grothendieck_topology.
- Grothendieck_topology subject Category:Sheaf_theory.
- Grothendieck_topology subject Category:Topos_theory.
- 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 label "Grothendieck-Topologie".
- Grothendieck_topology label "Topología de Grothendieck".
- Grothendieck_topology label "Топология Гротендика".
- Grothendieck_topology label "グロタンディーク位相".
- Grothendieck_topology sameAs Grothendieck-Topologie.
- Grothendieck_topology sameAs Topología_de_Grothendieck.
- Grothendieck_topology sameAs グロタンディーク位相.
- Grothendieck_topology sameAs 그로텐디크_위상.
- Grothendieck_topology sameAs m.03cv9.
- Grothendieck_topology sameAs Q1062242.
- Grothendieck_topology sameAs Q1062242.
- Grothendieck_topology wasDerivedFrom Grothendieck_topology?oldid=604214114.
- Grothendieck_topology isPrimaryTopicOf Grothendieck_topology.