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

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• Georg Tamme (Johannes Gutenberg-Universität Mainz)
• Tuesday 14 June 2022, 14:30-15:30
• Seminar Room 1, Newton Institute.

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KA2W01 - Algebraic K-theory, motivic cohomology and motivic homotopy theory

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 finite type over a field 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.

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

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