# Talk

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.