group scheme
A group scheme is a group object in the category
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 space do not form a group under the obvious choice for a group law.
We can view a group scheme G as a “group machine”: 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.
| 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 |