K-theory: from linear equations to the fundamental theorem

19/02/2021, 14:00 - 15:00 in online

Hüttemann, Thomas (QUB)

Abstract:

Algebraic K-theory is, at least initially, an attempt to understand how linear algebra works (or doesn’t) over general rings. A classical result by Bass, Heller, Swan and Quillen, the so-called fundamental theorem, expresses the K-theory of Laurent polynomial rings in terms of the K-theory of the ring of coefficients. I will explain the relevance of the lower K-groups for “linear algebra”, introduce the classical fundamental theorem, and explain how this can be generalised from Laurent polynomial rings to the large and interesting class of strongly Z-graded rings.