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algebraic cohomology

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  • Algebraic topology — is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism. In many situations this is too much to hope for… …   Wikipedia

  • Algebraic Geometry (book) — Algebraic Geometry is an influential algebraic geometry textbook written by Robin Hartshorne and published by Springer Verlag in 1977. It was the first extended treatment of scheme theory written as a text intended to be accessible to graduate… …   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

  • Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia

  • Algebraic K-theory — In mathematics, algebraic K theory is an important part of homological algebra concerned with defining and applying a sequence Kn(R) of functors from rings to abelian groups, for all integers n. For historical reasons, the lower K groups K0 and… …   Wikipedia

  • Algebraic torus — In mathematics, an algebraic torus is a type of commutative affine algebraic group. These groups were named by analogy with the theory of tori in Lie group theory (see maximal torus). The theory of tori is in some sense opposite to that of… …   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 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

  • Algebraic variety — This article is about algebraic varieties. For the term a variety of algebras , and an explanation of the difference between a variety of algebras and an algebraic variety, see variety (universal algebra). The twisted cubic is a projective… …   Wikipedia

  • Algebraic number theory — In mathematics, algebraic number theory is a major branch of number theory which studies the algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers O in an algebraic number… …   Wikipedia

  • Standard conjectures on algebraic cycles — In mathematics, the standard conjectures about algebraic cycles is a package of several conjectures describing the relationship of algebraic cycles and Weil cohomology theories. The original application envisaged by Grothendieck was to prove that …   Wikipedia

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