Projective bundle formula for Heller' relative K_0

Abstract

In this article, we study the Heller relative $K_0$ group of the map ${\mathbb{P}}_X^r\to {\mathbb{P}}_S^r,$ 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 $K_0({\mathbb{P}}_X^r\to {\mathbb{P}}_S^r)$ in terms of generators and relations, provided $X$ is affine and flat over $S.$

12 pages, Final version, accepted for publication