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The K-group of R-constructible Sheaves

Matvei Libine
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Abstract

Let Z be a smooth projective manifold. In these notes I will prove that the K-group of R-constructible sheaves is isomorphic to the free abelian group with one generator for each open semialgebraic subset $U$ (which I will denote by the same letter) modulo the Mayer-Vietoris relations: U + V - U^V - UvV = 0. I will prove it by showing that both groups in question are isomorphic to the group of all integer-valued semialgebraic functions on Z.

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Matvei Libine. 2002-12-25. The K-group of R-constructible Sheaves. https://arxiv.org/abs/math/0209034

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