# Algebraic Geometry Seminar

#### On the Arithmetic of Integral Representations of Finite Groups

Speaker: Dmitry Malinin, University of the West Indies, Kingston

Location: Warren Weaver Hall 201

Date: Wednesday, April 6, 2016, 5 p.m.

Synopsis:

We discuss arithmetic aspects of integral representations and some related questions: Schur groups, the embedding problem in Galois theory, Galois algebras, finite group schemes. D.K. Faddeev introduced generalized integral representations as a generalization of the theory of Steinitz and Chevalley. J.-P. Serre in his recent publication emphasized remarkable connections between integral irreducible representations of the group of quaternions and genus theory of Gauss and Hilbert, and the theory of Hilbert symbol. We consider generalizations of the concept of global irreducibility for arithmetic rings introduced by F. Van Oystaeyen and A.E. Zalesskii. We are also interested in certain constructions of integral representations; some of them use formal groups associated with torsion points of elliptic curves with supersingular reduction.