UAlberta Special Colloquium: Mathieu Florence

The Bloch-Kato-Milnor conjecture relates Galois cohomology to Milnor K-theory of fields. A celebrated proof of this result was furnished by Voevodsky. Motivic cohomology and Rost's norm varieties are key ingredients. They were tailored specifically for this purpose, under the guidance of Suslin. Today, this result is known as the Norm Residue Isomorphism Theorem. It is often considered to be internal to K-theory and to motivic cohomology. In this talk, I'll present a very different approach: deducing it from a much more elementary statement, about lifting representations of some profinite groups. I'll give some ideas/techniques for proving this statement. I'll try my best to make explanations accessible to a broad audience. The general philosophy, is to deduce everything from a formal version of Hilbert's Theorem 90- a basic fundamental result in Galois cohomology, similar to the Poincaré Lemma in topology. This is work in progress with Charles De Clercq.