About: Weil cohomology theory

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In algebraic geometry, a Weil cohomology or Weil cohomology theory is a cohomology satisfying certain axioms concerning the interplay of algebraic cycles and cohomology groups. The name is in honor of André Weil. Any Weil cohomology theory factors uniquely through the category of Chow motives, but the category of Chow motives itself is not a Weil cohomology theory, since it is not an abelian category.

Attributes	Values
rdf:type	yago:WikicatCohomologyTheories yago:WikicatTopologicalMethodsOfAlgebraicGeometry yago:Ability105616246 yago:Abstraction100002137 yago:Cognition100023271 yago:Explanation105793000 yago:HigherCognitiveProcess105770664 yago:Know-how105616786 yago:Method105660268 yago:Process105701363 yago:PsychologicalFeature100023100 yago:Theory105989479 yago:Thinking105770926
rdfs:label	Cohomologie de Weil (fr) ヴェイユコホモロジー (ja) Weil cohomology theory (en)
rdfs:comment	Une cohomologie de Weil est une théorie cohomologique des variétés algébriques, à coefficients dans un corps, satisfaisant un certain jeu d'axiomes. (fr) In algebraic geometry, a Weil cohomology or Weil cohomology theory is a cohomology satisfying certain axioms concerning the interplay of algebraic cycles and cohomology groups. The name is in honor of André Weil. Any Weil cohomology theory factors uniquely through the category of Chow motives, but the category of Chow motives itself is not a Weil cohomology theory, since it is not an abelian category. (en) 代数幾何学において、ヴェイユコホモロジー (Weil cohomology) あるいはヴェイユコホモロジー論 (Weil cohomology theory) とは、代数的サイクルとコホモロジー群の関係性についてのある公理系を満たすコホモロジーのことを言う。名前はアンドレ・ヴェイユ (André Weil) にちなむ。周モチーフを通してヴェィユコホモロジーが分解するという意味で、周モチーフの圏が普遍ヴェイユコホモロジー論である限りは、ヴェィユコホモロジー論がモチーフの理論で重要な役割を演じる。しかしながら、周モチーフの圏はアーベル圏ではないので、ヴェィユコホモロジー論をもたらさないことにも注意する必要がある。 (ja)
dcterms:subject	Cohomology theories Topological methods of algebraic geometry
Wikipage page ID	2960213 (xsd:integer)
Wikipage revision ID	1080821652 (xsd:integer)
Link from a Wikipage to another Wikipage	Princeton University Press De Rham cohomology Vector space Künneth theorem Cohomology theories GAGA Graded algebra Crystalline cohomology Simplicial homology André Weil Topological methods of algebraic geometry Étale cohomology Functor Poincaré duality Algebraic geometry Projective variety Hyperplane section Abelian category Characteristic (algebra) Cohomology Algebraic cycles Category (mathematics) Differential forms Chow motive Algebraic de Rham cohomology Betti cohomology K-algebra
Link from a Wikipage to an external page	https://archive.org/details/etalecohomology00miln
sameAs	Weil cohomology theory Weil cohomology theory Weil cohomology theory Weil cohomology theory Weil cohomology theory Weil cohomology theory
dbp:wikiPageUsesTemplate	dbt:Citation
has abstract	Une cohomologie de Weil est une théorie cohomologique des variétés algébriques, à coefficients dans un corps, satisfaisant un certain jeu d'axiomes. (fr) In algebraic geometry, a Weil cohomology or Weil cohomology theory is a cohomology satisfying certain axioms concerning the interplay of algebraic cycles and cohomology groups. The name is in honor of André Weil. Any Weil cohomology theory factors uniquely through the category of Chow motives, but the category of Chow motives itself is not a Weil cohomology theory, since it is not an abelian category. (en) 代数幾何学において、ヴェイユコホモロジー (Weil cohomology) あるいはヴェイユコホモロジー論 (Weil cohomology theory) とは、代数的サイクルとコホモロジー群の関係性についてのある公理系を満たすコホモロジーのことを言う。名前はアンドレ・ヴェイユ (André Weil) にちなむ。周モチーフを通してヴェィユコホモロジーが分解するという意味で、周モチーフの圏が普遍ヴェイユコホモロジー論である限りは、ヴェィユコホモロジー論がモチーフの理論で重要な役割を演じる。しかしながら、周モチーフの圏はアーベル圏ではないので、ヴェィユコホモロジー論をもたらさないことにも注意する必要がある。 (ja)
gold:hypernym	Cohomology
prov:wasDerivedFrom	wikipedia-en:Weil_cohomology_theory?oldid=1080821652&ns=0
page length (characters) of wiki page	5497 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Weil_cohomology_theory
is Link from a Wikipage to another Wikipage of	Kähler differential Crystalline cohomology Standard conjectures on algebraic cycles Étale cohomology Adequate equivalence relation Weil conjectures Cohomology Pierre Deligne Sheaf (mathematics) Weil cohomology
is Wikipage redirect of	Weil cohomology
is foaf:primaryTopic of	wikipedia-en:Weil_cohomology_theory

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