smooth cohomology

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• Cohomology with compact support — In mathematics, cohomology with compact support refers to certain cohomology theories, usually with some condition requiring that cocycles should have compact support. de Rham cohomology with compact support for smooth manifolds Given a manifold… …   Wikipedia

• Crystalline cohomology — In mathematics, crystalline cohomology is a Weil cohomology theory for schemes introduced by Alexander Grothendieck (1966, 1968) and developed by Pierre Berthelot (1974). Its values are modules over rings of Witt vectors over the base… …   Wikipedia

• De Rham cohomology — For Grothendieck s algebraic de Rham cohomology see Crystalline cohomology. In mathematics, de Rham cohomology (after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic… …   Wikipedia

• Étale cohomology — In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil… …   Wikipedia

• Deligne cohomology — In mathematics, Deligne cohomology is the hypercohomology of the Deligne complex of a complex manifold. It was introduced by Pierre Deligne in unpublished work in about 1972 as a cohomology theory for algebraic varieties that includes both… …   Wikipedia

• Weil cohomology theory — In algebraic geometry, a subfield of mathematics, 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 honour of André Weil. Weil… …   Wikipedia

• List of cohomology theories — This is a list of some of the ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectra. For other sorts of homology theories see the links at… …   Wikipedia

• Motivic cohomology — is a cohomological theory in mathematics, the existence of which was first conjectured by Alexander Grothendieck during the 1960s. At that time, it was conceived as a theory constructed on the basis of the so called standard conjectures on… …   Wikipedia

• Dolbeault cohomology — In mathematics, in particular in algebraic geometry and differential geometry, Dolbeault cohomology (named after Pierre Dolbeault) is an analog of de Rham cohomology for complex manifolds. Let M be a complex manifold. Then the Dolbeault… …   Wikipedia

• L² cohomology — In mathematics, L2 cohomology is a cohomology theory for smooth non compact manifolds M with Riemannian metric. It defined in the same way as de Rham cohomology except that one uses square integrable differential forms. The notion of square… …   Wikipedia

• Riemann-Roch theorem for smooth manifolds — In mathematics, a Riemann Roch theorem for smooth manifolds is a version of results such as the Hirzebruch Riemann Roch theorem or Grothendieck Riemann Roch theorem (GRR) without a hypothesis making the smooth manifolds involved carry a complex… …   Wikipedia