A group scheme over a base scheme 
is a group object
in the category of schemes
over 
. It consists of an 
-scheme 
with multiplication, identity, and inverse morphisms
satisfying the group axioms. Over an affine base 
, where 
is a commutative ring,
an affine group scheme is equivalently represented by a commutative 
-Hopf algebra.
Group Scheme
See also
Algebraic Group, Group, Hopf Algebra, SchemeExplore with Wolfram|Alpha
References
Waterhouse, W. C. Introduction to Affine Group Schemes. New York: Springer-Verlag, 1979.Cite this as:
Weisstein, Eric W. "Group Scheme." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GroupScheme.html