cohomology theory

cohomology theory
noun see cohomology

New Collegiate Dictionary. 2001.

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  • 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

  • Cohomology — In mathematics, specifically in algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co chain complex. That is, cohomology is defined as the abstract study of cochains, cocycles, and coboundaries.… …   Wikipedia

  • Cohomology operation — In mathematics, the cohomology operation concept became central to algebraic topology, particularly homotopy theory, from the 1950s onwards, in the shape of the simple definition that if F is a functor defining a cohomology theory, then a… …   Wikipedia

  • cohomology — noun Date: circa 1959 a part of the theory of topology in which groups are used to study the properties of topological spaces and which is related in a complementary way to homology theory called also cohomology theory • cohomological adjective …   New Collegiate Dictionary

  • Cohomology ring — In mathematics, specifically algebraic topology, the cohomology ring of a topological space X is a ring formed from the cohomology groups of X together with the cup product serving as the ring multiplication. Here cohomology is usually understood …   Wikipedia

  • cohomology — noun a) A theory associating a system of quotient groups to each topological space. b) A system of quotient groups associated to a topological space …   Wiktionary

  • 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

  • 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

  • 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

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