\(\mathcal A\)-schemes and Zariski-Riemann spaces (Q442634)

Summary: In this paper, we will investigate further properties of \(\mathcal A\)-schemes introduces in [Tak]. The category of \(\mathcal A\)-schemes possesses many properties of the category of coherent schemes, and in addition, it is co-complete and complete. There is the universal compactification, namely, the Zariski-Riemann space in the category of \(\mathcal A\)-schemes. We compare it with the classical Zariski-Riemann space, and characterize the latter by a left adjoint.