𝔸1-invariance of localizing invariants

Weibel proved that $p$ -inverted K-theory is $𝔸^{1}$ -invariant on $𝔽_{p}$ -schemes and K-theory with $ℤ ∕ p$ -coefficients is $𝔸^{1}$ -invariant on $ℤ [\frac{1}{p}]$ -schemes. We extend this result to all finitary localizing invariants of small stable $\infty$ -categories. Along the way we study the Frobenius and Verschiebung endofunctors defined by Tabuada and provide a categorical version of Stienstra’s projection formula.

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Keywords

noncommutative motives, localizing invariants, $\mathbb{A}^1$-invariance, Witt vectors

Mathematical Subject Classification

Primary: 13F35, 14F42, 18F25

Milestones

Received: 7 January 2023

Revised: 19 February 2024

Accepted: 3 March 2024

Published: 25 May 2024

Authors

Vladimir Sosnilo
Faculty of Mathematics Universität Regensburg Regensburg Germany

Vol. 9, No. 1, 2024

Vladimir Sosnilo

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors