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October 2020 Projective bundle formula for Heller's relative $K_{0}$
Vivek Sadhu
Kodai Math. J. 43(3): 591-602 (October 2020). DOI: 10.2996/kmj/1605063630

Abstract

In this article, we study the Heller relative $K_{0}$ group of the map $\mathbf{P}_{X}^{r} \to \mathbf{P}_{S}^{r}$, where $X$ and $S$ are quasi-projective schemes over a commutative ring. More precisely, we prove that the projective bundle formula holds for Heller's relative $K_{0}$, provided $X$ is flat over $S$. As a corollary, we get a description of the relative group $K_{0}(\mathbf{P}_{X}^{r} \to \mathbf{P}_{S}^{r})$ in terms of generators and relations, provided $X$ is affine and flat over $S$.

Citation

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Vivek Sadhu. "Projective bundle formula for Heller's relative $K_{0}$." Kodai Math. J. 43 (3) 591 - 602, October 2020. https://doi.org/10.2996/kmj/1605063630

Information

Published: October 2020
First available in Project Euclid: 11 November 2020

MathSciNet: MR4173166
Digital Object Identifier: 10.2996/kmj/1605063630

Rights: Copyright © 2020 Tokyo Institute of Technology, Department of Mathematics

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Vol.43 • No. 3 • October 2020
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