Higher K-theory of polynomial categories

Details Higher K-theory of polynomial categories Higher K-theory of polynomial categories

2011-04-21

arxiv.org/abs/1104.4240v1

Mathematics

Commutative Algebra

13 pages

Scientific paper

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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