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Towards Vorst's conjecture in positive characteristic

Part of: Higher algebraic $K$-theory

Published online by Cambridge University Press:  20 May 2021

Moritz Kerz ,
Florian Strunk  and
Georg Tamme
Moritz Kerz
Affiliation:
Fakultät für Mathematik, Universität Regensburg, 93040Regensburg, Germanymoritz.kerz@ur.de
Florian Strunk
Affiliation:
Fakultät für Mathematik, Universität Regensburg, 93040Regensburg, Germanyflorian.strunk@ur.de
Georg Tamme
Affiliation:
Institut für Mathematik, Fachbereich 08, Johannes Gutenberg-Universität Mainz, 55099Mainz, Germanygeorg.tamme@uni-mainz.de
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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.

Keywords

Cartier isomorphismVorst's conjecturevaluation ringK-regularity

MSC classification

Primary: 19D35: Negative $K$-theory, NK and Nil
Secondary: 19D55: $K$-theory and homology; cyclic homology and cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 157 , Issue 6 , June 2021 , pp. 1143 - 1171
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Copyright
© The Author(s) 2021

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Footnotes

The authors are supported by the DFG through CRC 1085 Higher Invariants (Universität Regensburg).

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