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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 ...

...c geometry, the '''cohomology of a stack''' is a generalization of [[étale cohomology]]. In a sense, it is a theory that is coarser than the [[Chow group of a st ...equivariant cohomology]]. For example, [[Borel's theorem]] states that the cohomology ring of a [[classifying stack]] is a polynomial ring. ...

...c ''p'' {{harvtxt|Ogus|1975}} showed that it is closely related to [[etale cohomology]] with mod ''p'' coefficients, a theory known to have undesirable prop ...ive-date=2022-02-08 |year=1968 |volume=3 |chapter=Crystals and the de Rham cohomology of schemes |pages=306–358}}. ...

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

...el''' is a [[differential graded algebra]] that computes the [[equivariant cohomology]] of a [[topological space|space]]. ...ures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories'', {{arxiv|hep-th/9411210}}, 1994. ...

...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>. ...

...a [[continuous mapping]] of spaces one obtains a [[ring homomorphism]] on cohomology rings, which is contravariant. Specifically, given a sequence of cohomology groups ''H''^''k''(''X'';''R'') on ''X'' with coefficients in a [ ...

...''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 ...

{{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 ...

In mathematics, '''Brown–Peterson cohomology''' is a [[generalized cohomology theory]] introduced by Brown–Peterson cohomology BP is a summand of MU_(''p''), which is [[complex cobordism]] MU ...

...l equation]] on a [[closed manifold]]). They are likewise used in [[group cohomology]]. In [[autonomous system (mathematics)|autonomous]] [[dynamical system]]s * [[Čech cohomology]] ...

...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== ...

...bitrary [[topological space]]s.<ref>"Modern Differential Geometry in Gauge Theories: Maxwell fields", Anastasios Mallios, Springer, 2005, {{ISBN|978-0-8176-437 ...iv.org/abs/math.DG/0406540 Space-time foam dense singularities and de Rham cohomology], A Mallios, EE Rosinger, Acta Applicandae Mathematicae, 2001 ...

...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]]. ...

In [[mathematics]], '''elliptic cohomology''' is a [[cohomology theory]] in the sense of [[algebraic topology]]. It is related to [[ellipti ...ated these to (conjectural) index theory on [[free loop]] spaces. Elliptic cohomology, invented in its original form by Landweber, Stong and [[Douglas Ravenel|Ra ...

...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. ...

...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 ...

...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. ...

{{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 ...