In number theory, Iwasawa theory is a Galois module theory of ideal class groups, started by Kenkichi Iwasawa, in the 1950s, as part of the theory of cyclotomic fields. In the early 1970s, Barry Mazur thought about generalizations of Iwasawa theory to Abelian Varieties. Later, in the early 90s, Ralph Greenberg has suggested an Iwasawa theory for motives.