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Chow group

In algebraic geometry, the Chow groups (named after Wei-Liang Chow by Claude Chevalley (1958)) of an algebraic variety over any field are algebro-geometric analogs of the homology of a topological space. The elements of the Chow group are formed out of subvarieties (so-called algebraic cycles) in a similar way to how simplicial or cellular homology…

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Overview

Rational equivalence and Chow groups

The Chow ring

Examples

Functoriality

Cycle maps

Relation to K-theory

Conjectures

Variants

History

Advanced

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Map overview Semantic statistics

Chow group

Nodes126
Edges125
Triples71
Avg. degree1.98
Density0.015873
Components1

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Chow group

Top relations

related to Conjectures · 21
Chow group → Bass, Beilinson, Bloch, CHn-1, Chow, Finiteness, For, Hodge, It, K-theory, Kato, L-function, L-functions, Moreover, Ql, Some, Tate, The, The Bloch, The Mordell
related to Relation to K-theory · 12
Chow group → An, As, Chern, CHi, Chow, Grothendieck, K0, Namely, Riemann, Roch, The Chern, This
related to history · 11
Chow group → Chow, Chow's, For, Francesco Severi, Fulton, In, Jacobian, MacPherson, Rational, Starting, Wei-Liang Chow
related to Remarks · 7
Chow group → Chow, For, Mordell, Then, Thus, Weil, When
related to The Chow ring · 7
Chow group → CH, Chow, For, Namely, The, Then, When
related to Cycle maps · 5
Chow group → Borel, Chow, First, Moore, There
related to Other variants · 4
Chow group → Arakelov-theoretical, Arithmetic Chow, Chow, The

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Important terminology

chow displaystyle groups ring group smooth variety field algebraic cycles theory scheme projective cycle cohomology intersection example subvarieties homomorphism ch

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
motivic cohomology map to the operational Chow ring.Other variantsArithmetic Chow groups are an amalgamation of Chow groups of varieties over Q together with a component encoding Arakelov-theoretical informationinstance ofother theories0.80text
that isinstance ofother theories0.80text
differential forms on the associated complex manifold.The theory of Chow groups of schemes of finite type over a field extends easily to that of algebraic spacesinstance ofother theories0.80text
motivic cohomology map to the operational Chow ringinstance ofother theories0.80text
Chow grouprelated to ConjecturesSome0.60section
Chow grouprelated to ConjecturesChow0.60section
Chow grouprelated to ConjecturesFor0.60section
Chow grouprelated to ConjecturesThe Mordell0.60section
Chow grouprelated to ConjecturesWeil0.60section
Chow grouprelated to ConjecturesCHn-10.60section
Chow grouprelated to ConjecturesIt0.60section
Chow grouprelated to ConjecturesThe Bloch0.60section

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