group scheme
A group scheme is a group object in the category of schemes. Similarly, if is a scheme, a group scheme over is a group object in the category of schemes over .
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 space do not form a group under the obvious choice for a group law.
We can view a group scheme as a “group machine”: given a ring , the set of -points of forms a group. If is a scheme that is not affine, we can nevertheless interpret as a family of groups fibred over .
Title | group scheme |
Canonical name | GroupScheme |
Date of creation | 2013-03-22 14:11:13 |
Last modified on | 2013-03-22 14:11:13 |
Owner | archibal (4430) |
Last modified by | archibal (4430) |
Numerical id | 4 |
Author | archibal (4430) |
Entry type | Definition |
Classification | msc 14K99 |
Classification | msc 14A15 |
Classification | msc 14L10 |
Classification | msc 20G15 |
Related topic | Group |
Related topic | GroupVariety |
Related topic | Category |
Related topic | GroupObject |
Related topic | GroupSchemeOfMultiplicativeUnits |
Related topic | VarietyOfGroups |