Seminar Room 1, Newton Institute
Commutative regular local rings play an important role in classical algebraic geometry and are precisely the commutative local Noetherian rings of finite global dimension. Iwasawa algebras form a natural class of complete semilocal Noetherian rings with good homological properties, which are noncommutative in general. These algebras have applications in number theory and have connections to Lie theory, but their algebraic structure is still rather mysterious. I will present an overview of the known ring-theoretic properties of Iwasawa algebras.