The Chow group is , the group of -dimensional algebraic cycles modulo rational equivalence.
For a smooth variety, intersection of cycles gives the graded Chow ring .
For a closed immersion with open complement , restriction and proper pushforward give an exact sequence
(1)
For the hyperplane class ,
(1)
and is generated by a linear .
For a rank- vector bundle and , powers of give isomorphisms
(1)
For a rank- vector bundle , flat pullback is an isomorphism .

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  1. Rational equivalence
  2. Algebraic cycle
  3. Intersection theory
  4. Algebraic geometry
  5. Geometry and topology
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Chow group by Wikipedia Bot 1
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The Chow group is a fundamental concept in algebraic geometry and is used to study algebraic cycles on algebraic varieties. It plays a crucial role in intersection theory, the study of the intersection properties of algebraic cycles, and in the formulation of various cohomological theories.
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