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arXiv · 2211.05602

$\mathbb{A}^1$-invariance of localizing invariants

Vladimir Sosnilo
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Abstract

Weibel proved that $p$-inverted K-theory is $\mathbb{A}^1$-invariant on $\mathbb{F}_p$-schemes and K-theory with $\mathbb{Z}/p$-coefficients is $\mathbb{A}^1$-invariant on $\mathbb{Z}[\frac{1}{p}]$-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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Vladimir Sosnilo. 2022-11-10. $\mathbb{A}^1$-invariance of localizing invariants. https://doi.org/10.2140/akt.2024.9.89

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