Georg Tamme: A version of Vorst's conjecture in positive and mixed characteristic

This is joint work with Moritz Kerz and Florian Strunk. It is a classical result that the K-theory of regular Noetherian rings is A1-invariant. Vorst conjectured a converse statement: If A is essentially of nite type over a eld and Kd+1-regular (i.e. Kd+1(A) = Kd+1(A[T1, ..., Tr]) for all r) where d = dim(A), then A is regular. He proved this conjecture in case dim(A) = 1. The general case for Q-algebras was proven by Cortiñas-Haesemeyer-Weibel. In the talk I will discuss the case of Fp-algebras and a mixed characteristic version for curves.