Rendiconti del Seminario Matematico della Università di Padova

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Volume 127, 2012, pp. 121–177
DOI: 10.4171/RSMUP/127-8

$\mathscr{A}$-Schemes and Zariski-Riemann Spaces

Satoshi Takagi[1]

(1) Advanced Mathematical Institute, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, 558-8585, Osaka, Japan

In this paper, we will investigate further properties of $\mathscr{A}$-schemes introduced in [Tak]. The category of $\mathscr{A}$-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 $\mathscr{A}$-schemes. We compare it with the classical Zariski-Riemann space, and characterize the latter by a left adjoint.

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Takagi Satoshi: $\mathscr{A}$-Schemes and Zariski-Riemann Spaces. Rend. Sem. Mat. Univ. Padova 127 (2012), 121-177. doi: 10.4171/RSMUP/127-8