多项式范畴的高阶K-理论
Higher K-theory of polynomial categories
摘要：
本文的主要定理是：如果$\cA$是Noether范畴且有足够的投射对象，则从交换范畴$\cA$到它的Schlichting意义下的多项式范畴$-\otimes_{\cA}\bbZ[t]:\cA \to \cA[t]$的基变换函子在它们的$K$ -理论上诱导同构.主要定理隐含了一个众所周知的事实，即$K'$ -理论对Noether格式的$\mathbb{A}^1$ -同伦不变性.
英文摘要：
The main theorem in this paper is that the base change functor from an abelian category $\cA$ to its polynomial category in the sense of Schlichting $-\otimes_{\cA}\bbZ[t]:\cA \to \cA[t]$ induces an isomorphism on their $K$-theories if $\cA$ is noetherian and has enough projective objects. The main theorem implies the well-known fact that $\mathbb{A}^1$-homotopy invariance of $K'$-theory for noetherian schemes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
