Last Updated
：2025/12/05
Chow group
Noun
(mathematics)
The
Chow
groups
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
groups
are
formed
out
of
subcomplexes.
Japanese Meaning
チョウ群：任意の体上の代数多様体に対して定義される、位相空間のホモロジーの代数幾何学的な類似物。部分多様体（すなわち代数的サイクル）を用いて構成され、しばしば代数多様体の幾何学的性質を捉えるための道具として用いられる。
Sense（1）
(mathematics)
The
Chow
groups
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
groups
are
formed
out
of
subcomplexes.
（ plural ）
Quizzes for review
(mathematics) The Chow groups 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 groups are formed out of subcomplexes.
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See correct answer
Chow group
When studying the intersection theory on an algebraic variety, the Chow group provides a natural setting for comparing algebraic cycles.
See correct answer
When studying the intersection theory on an algebraic variety, the Chow group provides a natural setting for comparing algebraic cycles.
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English - English
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