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...tion (mathematics)|connection]], or equivalently of a 2-class in [[Deligne cohomology]]. ...hich is an element of <math>H^2(M, \mathbb{Z})</math>, the second integral cohomology of <math>M</math>. ...

...for [[algebraic variety|algebraic varieties]] that includes both ordinary cohomology and [[intermediate Jacobian]]s. For introductory accounts of Deligne cohomology see {{harvtxt|Brylinski|2008|loc=section 1.5}}, {{harvtxt|Esnault|Viehweg|1 ...

...dified BF theories as [[topological quantum field theory|topological field theories]], which give rise to [[Linking number|link invariants]] in 3 dimensions, 4 {{Quantum field theories}} ...

...m for a number of statements about restrictions on possible values of [[L2 cohomology|<math>l^2</math>-Betti numbers]]. ...s as [[von Neumann dimension]]s of the resulting {{nowrap|<math>l^2</math>-cohomology}} groups, and computed several examples, which all turned out to be [[ratio ...

...Axioms and generalized cohomology theories|Generalized homology/cohomology theories]].<ref>{{cite book |last1=Adams |first1=Frank |title=Stable Homotopy and Ge ...

...am cohomology]] to [[singular cohomology]] of complex varieties or [[étale cohomology]] of ''p''-adic varieties. ...e-Arakelov theory of elliptic curves: global discretization of local Hodge theories | url=http://www.kurims.kyoto-u.ac.jp/~motizuki/The%20Hodge-Arakelov%20Theo ...

...r bundle]]s; this is closely related to the condition that a [[generalized cohomology theory]] has a [[complex orientation]]. ...riented cohomology theories from algebraic cobordism to any other oriented cohomology theory. ...

...own as a [[Leray cover]].) However, for the purposes of computing the Čech cohomology it suffices to have a more relaxed definition of a good cover in which all [[Category:Cohomology theories]] ...

...the cohomology group <math>H^2(M)</math> for the fiber bundle ''M''. The cohomology arises from the idea of classifying all possible gauge [[field strength]]s [[Category:Gauge theories]] ...

...alois representation]]s that may be derived by more abstract means. Galois cohomology accounts for the way in which taking Galois-invariant elements fails to be .... Firstly, Galois cohomology appeared as the foundational layer of [[étale cohomology]] theory (roughly speaking, the theory as it applies to zero-dimensional sc ...

...that, as far as [[Étale cohomology|etale]] (or [[Flat cohomology|flat]]) [[cohomology]] is concerned, the [[ring of integers]] in a [[Algebraic number field|numb Here, ''H^r''(''X,F'') is the ''r''-th [[étale cohomology]] group of the [[scheme (mathematics)|scheme]] ''X'' with values in ''F,'' ...

{{Short description|Cohomology theory for topological spaces}} ...larly in [[algebraic topology]], '''Alexander–Spanier cohomology''' is a [[cohomology]] theory for [[topological space]]s. ...

=== Spectrum and generalized cohomology === {{main|Spectrum (algebraic topology)|Generalized cohomology}} ...

{{Short description|Properties that homology theories of topological spaces have in common}} ...ilenberg–Steenrod axioms''' are properties that [[homology theory|homology theories]] of [[topological space]]s have in common. The quintessential example of a ...

...used in [[algebraic geometry]]. It is used to define the theory of '''flat cohomology'''; it also plays a fundamental role in the theory of [[descent (category t Flat cohomology was introduced by Grothendieck in about 1960.<ref>*{{Citation | last1=Groth ...

...action of a topological group <math>G</math> is defined as the ordinary [[cohomology ring]] with coefficient ring <math>\Lambda</math> of the [[homotopy quotien ...logy ring of the [[classifying space]] <math>BG</math> (that is, the group cohomology of <math>G</math> when ''G'' is finite.) If ''G'' acts freely on ''X'', the ...

...ntroduced by Dubrovin,<ref>B. Dubrovin: ''Geometry of 2D topological field theories.'' In: Springer LNM, 1620 (1996), pp.&nbsp;120–348.</ref> is a flat [[Rie ...lly in the subject of [[symplectic topology]], more specifically [[quantum cohomology]]. The broadest definition is in the category of Riemannian [[supermanifol ...

...leading to the [[Hodge decomposition]] of the [[Georges de Rham|de Rham]] cohomology. ...term, which is the <math>E_1</math>-page of the spectral sequence, is the cohomology with values in the sheaf of [[Holomorphic function|holomorphic]] [[differen ...

...es some slightly weaker theories derived from it, such as [[Brown–Peterson cohomology]] or [[Morava K-theory]], that are easier to compute. The generalized homology and cohomology complex cobordism theories were introduced by {{harvs|txt|last=Atiyah|first=Michael|authorlink=Michael ...

...roup]] in [[group cohomology]].<ref>{{nlab|id=group+cohomology|title=group cohomology}}</ref> ...group]]s<ref> {{nlab|id=nonabelian+group+cohomology|title=nonabelian group cohomology}}</ref> ...