Christian Dahlhausen
We study relative algebraic K-theory of admissible Zariski-Riemann spaces and prove that it is equivalent to G-theory and satisfies homotopy invariance. Moreover, we provide an example of a non-noetherian abelian category whose negative K-theory vanishes.
This paper contains 8 sections, 30 theorems, 60 equations.
Theorem 1
Let $X$ be a reduced, divisorial, and noetherian scheme and let $U$ be a dense open subset of $X$. Denote by $\tilde{Z}$ the complement of $U$ in $\langle X\rangle_U$. Then Moreover, if $U$ is regular, then where $\mathop{\mathrm{G}}\nolimits(\langle X\rangle_U) := \mathop{\mathrm{K}}\nolimits(\mathrm{Mod}^\mathrm{fp}(\langle X\rangle_U))$ (Definition G-theory-ZR--def).
