 Group scheme

A group scheme over a base scheme $S$ is an $S$-scheme $G$ with multiplication $m:G{\times }_{S}G\to G$, an identity section $e:S\to G$, and inversion $i:G\to G$ satisfying the group axioms as equalities of morphisms.

In algebraic geometry and number theory, a **group scheme** is a scheme that has the structure of a group, in the sense that it supports the operations of multiplication and inversion in a way that is compatible with the geometric structure.