Serre group

In mathematics, the Serre group S is the pro-algebraic group whose representations correspond to CM-motives over the algebraic closure of the rationals, or to polarizable rational Hodge structures with abelian Mumford–Tate groups. It is a projective limit of finite dimensional tori, so in particular is abelian. It was introduced by Serre (1968). It is a subgroup of the Taniyama group.

There are two different but related groups called the Serre group, one the connected component of the identity in the other. This article is mainly about the connected group, usually called the Serre group but sometimes called the connected Serre group. In addition one can define Serre groups of algebraic number fields, and the Serre group is the inverse limit of the Serre groups of number fields.