| dbo:abstract |
In der Algebraischen Geometrie, einem Teilgebiet der Mathematik, sind Chow-Gruppen eine wichtige Invariante von Varietäten. (de) In algebraic geometry, the Chow groups (named after Wei-Liang Chow by Claude Chevalley) 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. When the variety is smooth, the Chow groups can be interpreted as cohomology groups (compare Poincaré duality) and have a multiplication called the intersection product. The Chow groups carry rich information about an algebraic variety, and they are correspondingly hard to compute in general. (en) 代数幾何学のチャウ群（チャウぐん、英: Chow group）とは、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群の代数幾何学的な類似物である。単体や胞体から単体ホモロジー群やを作るのと同じやり方で、チャウ群は部分多様体（いわゆる代数的サイクル）から作られる。多様体がな場合にはチャウ群は（ポアンカレ双対性によって）コホモロジー群と思うこともでき、交叉積と呼ばれる乗法を持つ。チャウ群は代数多様体に関する豊富な情報を持つが、一般的に計算するのは困難である。 (ja) 代數幾何中，代數簇的周環（得名於周煒良）是簇作為拓撲空間的的替代品：子簇（所謂）構成了它的元素，而其乘法結構來自子簇的相交。事實上，兩環間有一自然映射，它保持了二者都有的幾何概念（例如陳類、相交配對以及龐加萊對偶）。周環的優勢在於其幾何定義不需使用非代數概念。並且，使用了純拓撲情況下不可用的代數工具後，某些兩環都有的構造在周環中更簡單。 (zh) |
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Claude Chevalley (en) |
| dbp:first |
Claude (en) |
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Chevalley (en) |
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1958 (xsd:integer) |
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dbc:Chinese_mathematical_discoveries dbc:Topological_methods_of_algebraic_geometry dbc:Algebraic_geometry dbc:Intersection_theory |
| rdfs:comment |
In der Algebraischen Geometrie, einem Teilgebiet der Mathematik, sind Chow-Gruppen eine wichtige Invariante von Varietäten. (de) In algebraic geometry, the Chow groups (named after Wei-Liang Chow by Claude Chevalley) 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. When the variety is smooth, the Chow groups can be interpreted as cohomology groups (compare Poincaré duality) and have a multiplication called the intersection product. The Chow groups carry rich information about an algebraic variety, and they are correspondingly hard to compute in general. (en) 代数幾何学のチャウ群（チャウぐん、英: Chow group）とは、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群の代数幾何学的な類似物である。単体や胞体から単体ホモロジー群やを作るのと同じやり方で、チャウ群は部分多様体（いわゆる代数的サイクル）から作られる。多様体がな場合にはチャウ群は（ポアンカレ双対性によって）コホモロジー群と思うこともでき、交叉積と呼ばれる乗法を持つ。チャウ群は代数多様体に関する豊富な情報を持つが、一般的に計算するのは困難である。 (ja) 代數幾何中，代數簇的周環（得名於周煒良）是簇作為拓撲空間的的替代品：子簇（所謂）構成了它的元素，而其乘法結構來自子簇的相交。事實上，兩環間有一自然映射，它保持了二者都有的幾何概念（例如陳類、相交配對以及龐加萊對偶）。周環的優勢在於其幾何定義不需使用非代數概念。並且，使用了純拓撲情況下不可用的代數工具後，某些兩環都有的構造在周環中更簡單。 (zh) |
| rdfs:label |
Chow-Gruppe (de) Chow group (en) チャウ群 (ja) 저우 환 (ko) 周環 (zh) |
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