Towards Vorst's conjecture in positive characteristic

Abstract

Vorst's conjecture relates the regularity of a ring with the ${\mathbb{A}}^1$-homotopy invariance of its $K$-theory. We show a variant of this conjecture in positive characteristic.

v1: 23 pages; v2: added a result for curves in mixed characteristic, 30 pages; v3: final version, 31 pages