Let be a variety (an affine (http://planetmath.org/AffineVariety), projective (http://planetmath.org/ProjectiveVariety), or quasi-projective variety). We say is a group variety if is provided with morphisms of varieties:
and if these morphisms make the elements of into a group.
Just as schemes generalize varieties, group schemes generalize group varieties. When dealing with situations in positive characteristic, or with families of group varieties, often they are more appropriate.
There is also a (not very closely related) concept in group theory of a “variety of groups (http://planetmath.org/VarietyOfGroups)”.
|Date of creation||2013-03-22 14:09:37|
|Last modified on||2013-03-22 14:09:37|
|Last modified by||archibal (4430)|