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...ohomology''', introduced by [[Glen E. Bredon]], is a type of [[equivariant cohomology]] that is a [[contravariant functor]] from the [[category (mathematics)|cat | title = Equivariant cohomology theories ...

...m]]. Typical theories it studies include: [[complex K-theory]], [[elliptic cohomology]], [[Morava K-theory]] and [[Topological modular forms|tmf]]. *[[Elliptic cohomology]] ...

...algebras]] of smooth [[vector field]]s. It differs from the [[Lie algebra cohomology]] of Chevalley-Eilenberg in that its cochains are taken to be continuous mu ...e journal |last=Gel'fand |first=I. M. |last2=Fuks |first2=D. B. |title=The cohomology of the Lie algebra of formal vector fields |journal=Mathematics of the USSR ...

...charov|year=1995}} suggesting that the [[cohomology]] of certain [[Motivic cohomology|motivic complex]]es coincides with pieces of [[Algebraic K-theory|K-groups] ...ured that ''i''-th cohomology of this complex is isomorphic to the motivic cohomology group <math>H^i_{mot}(F,\mathbb Q(n))</math>. ...

...topological space]]s and a ring ''R'', the '''pullback''' along ''f'' on [[cohomology theory]] is a [[graded ring|grade]]-preserving ''R''-[[algebra homomorphism ...ifold]]s, ''R'' the field of real numbers, and the cohomology is [[de Rham cohomology]], then the pullback is induced by the pullback of [[differential form]]s. ...

In [[mathematics]], the '''Koszul cohomology''' groups <math>K_{p,q}(X,L)</math> are [[group (mathematics)|group]]s asso ...szul cohomology, {{harvtxt|Eisenbud|2005}} gives an introduction to Koszul cohomology, and {{harvtxt|Aprodu|Nagel|2010}} gives a more advanced survey. ...

{{short description|Result in algebraic K-theory relating Chow groups to cohomology}} ...th variety ''X'' over a [[field (mathematics)|field]] is isomorphic to the cohomology of ''X'' with coefficients in the K-theory of the structure sheaf <math>\ma ...

...''complex orientation'''. The notion is central to Quillen's work relating cohomology to [[formal group law]]s.{{citation needed|date=October 2013}}<!-- a bit va *An ordinary cohomology with any coefficient ring ''R'' is complex orientable, as <math>\operatorna ...

==Twisted Poincaré duality for de Rham cohomology== ...tion maps. As a [[flat vector bundle|flat line bundle]], it has a de Rham cohomology, denoted by ...

...matics, '''cohomology with compact support''' refers to certain cohomology theories, usually with some condition requiring that cocycles should have compact su ==Singular cohomology with compact support== ...

...nrod axioms]] for [[homology (mathematics)|homology]] to give axioms for [[cohomology]]. It is named after [[Beno Eckmann]] and [[Peter Hilton]]. ...um (homotopy theory)|spectra]], which give rise to [[cohomology|cohomology theories]]. ...

...algebra]], '''Grothendieck local duality''' is a [[duality theorem]] for [[cohomology]] of [[module (mathematics)|modules]] over [[local ring]]s, analogous to [[ where ''H''_''m'' is a [[local cohomology]] group. ...

...]], several types of products are defined on homological and cohomological theories. ...of [[differential form]]s in [[de Rham cohomology]]. It makes the singular cohomology of a connected manifold into a unitary supercommutative ring. ...

...thfrak{k})</math> is said to be '''Cartan''' if the relative [[Lie algebra cohomology]] ...incipal Bundles and Homogeneous Spaces |series=Connections, Curvature, and Cohomology |volume=3 |chapter-url=https://books.google.com/books?id=c724LN914AwC&pg=PA ...

...from the category of spaces to the category of [[abelian group]]s, while a cohomology theory is a [[contravariant functor]] from the category of (nice) spaces to Unlike a homology theory or a cohomology theory, a bivariant class is defined for a map not a space. ...

{{Short description|Theory of cohomology for commutative rings}} ...]]s which is closely related to the [[cotangent complex]]. The first three cohomology groups were introduced by {{harvs|txt|last1=Lichtenbaum| first1=Stephen|aut ...

...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 ...

...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 ...

...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]] ...

In [[Galois cohomology]], '''local Tate duality''' (or simply '''local duality''') is a [[Duality ...ristic formula]] provide a versatile set of tools for computing the Galois cohomology of local fields. ...