ALGB Seminar: Julia Semikina (University of Bonn)
Title: G-theory of group rings for finite groups
Abstract: The G-theory of a ring R is defined as Quillen's K-theory of the category of finitely generated R-modules. In this talk we will review the Hambleton-Taylor-Williams conjecture for the decomposition of Gn(ZG) as a direct sum of the G-theory of certain maximal orders in the factors of QG, where G is any finite group. We will explain the connection between the conjecture and the Brauer-Nesbitt theorem on blocks of defect zero, and show that the solvable group SL(2, F3) is a counterexample to the conjectured decomposition in degree n=1. Nevertheless, we will present some results supporting the weaker version of the conjecture.