# CANCELLED On a conjecture of Vorst

KAHW02 - Algebraic K-theory, motivic cohomology and motivic homotopy theory

Quillen proved that algebraic K-theory is A^1-invariant on regular noetherian schemes. Vorst’s conjecture is a partial converse. Let k be a field, and let A be a k-algebra essentially of finite type and of dimension d. Vorst’s conjecture predicts that if K_{d+1}(A) = K_{d+1}(A[t_1, \dots, t_m]) for all positive integers m, then A is regular. This conjecture was proven by Cortinas, Haesemeyer, and Weibel in case k has characteristic 0. In the talk, I will explain the proof of a slightly weaker version of the conjecture if k has positive characteristic. Joint work with Moritz Kerz and Florian Strunk.

This talk is part of the Isaac Newton Institute Seminar Series series.