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单词 GroupScheme
释义

group scheme


A group scheme is a group object in the categoryMathworldPlanetmath of schemes. Similarly, if S is a scheme, a group scheme over S is a group object in the category of schemes over S.

As usual with schemes, the points of a group scheme are not the whole story. For example, a group scheme may have only one point over its field of definition and yet not be trivial. The points of the underlying topological spaceMathworldPlanetmath do not form a group under the obvious choice for a group law.

We can view a group scheme G as a “group machineMathworldPlanetmath”: given a ring R, the set of R-points of G forms a group. If S is a scheme that is not affine, we can nevertheless interpret G as a family of groups fibred over S.

Titlegroup scheme
Canonical nameGroupScheme
Date of creation2013-03-22 14:11:13
Last modified on2013-03-22 14:11:13
Ownerarchibal (4430)
Last modified byarchibal (4430)
Numerical id4
Authorarchibal (4430)
Entry typeDefinition
Classificationmsc 14K99
Classificationmsc 14A15
Classificationmsc 14L10
Classificationmsc 20G15
Related topicGroup
Related topicGroupVariety
Related topicCategory
Related topicGroupObject
Related topicGroupSchemeOfMultiplicativeUnits
Related topicVarietyOfGroups
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更新时间:2025/5/4 22:53:39