An introduction to Milnor-Witt K-theory

Speaker: Dr Kevin Hutchinson (UCD)

Time: 4:00PM
Date: Wed 2nd May 2007

Location: Mathematical Sciences Seminar Room

This is primarily an expository talk on the work of Fabien Morel. Milnor-Witt K-theory arises as a graded algebra of homomorphisms - or cohomology operations - in the ' A^1-homotopy category'. The Milnor-Witt K-theory of a field has a particularly elegant presentation, due to Morel and M. Hopkins, which relates it to Milnor K-theory and to the powers of thefundamental ideal in the Witt Ring of the field. I will discuss therelation to Milnor conjecture and to the results of Arason and Elman on the powers of the fundamental ideal.

Time permitting, I will discuss ongoing work with L. Tao on the relation to the homology of special linear groups.

(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)