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arXiv · 1104.4240

Higher K-theory of polynomial categories

Satoshi Mochizuki·Akiyoshi Sannai
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Abstract

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.

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Satoshi Mochizuki, Akiyoshi Sannai. 2011-04-21. Higher K-theory of polynomial categories. https://arxiv.org/abs/1104.4240

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