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 $\mathbb{Z}\left[\frac{1}{p}\right]$-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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