论文标题
美元
$\mathbb{A}^1$-invariance of localizing invariants
论文作者
论文摘要
微作者证明，$ p $ inverted k-theory是$ \ mathbb {a}^1 $ -Invariant on $ \ mathbb {f} _p $ -schemes和k-theory and k-theory，带有$ \ mathbb {z}/p $ - coeffients是$ $ \ mathbb {z} [\ frac {1} {p}] $ - schemes。我们将此结果扩展到所有稳定$ \ infty $ - 类别的所有限制本地化不变。在途中，我们研究了Tabuada定义的Frobenius和Verschiebung内of起点，并提供了Stienstra投影公式的绝对版本。
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.
