Modul: MAT770 Oberseminar: Algebraische Geometrie

## On a conjecture of Vorst

Dr. Florian Strunk talk

Speaker invited by: Prof. Dr. Joseph Ayoub

**Date:** 04.11.19 **Time:** 13.15 - 14.45 **Room:** Y27H25

Quillen proved that the \(K\)-groups of a noetherian regular ring are \(\mathbb{A}^1\)-homotopy invariant. Vorst's conjecture is the (possibly slightly stronger) converse of this statement for schemes essentially of finite type over a field. This conjecture was shown by Cortiñas-Haesemeyer-Weibel in characteristic zero and Geisser-Hesselholt (without 'essentially') over a perfect infinite field of positive characteristic assuming strong resolution of singularities. We remove this assumption and question the necessity of the condition to be of finite type over a field for the conjecture to hold. This is joint work with Moritz Kerz and Georg Tamme.