Birational spaces

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• 作者：Uri Brezner ^{uri.brezner@mail.huji.ac.il" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Algebraic geometry
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：469
• 期：Complete
• 页码：30-76
• 全文大小：705 K

文摘

In this paper we construct the category of birational spaces as the category in which the relative Riemann–Zariski spaces of an id="bbr0090">[9]a>an> are naturally included. Furthermore we develop an analogue of Raynaud's theory. We prove that the category of quasi-compact and quasi-separated birational spaces is naturally equivalent to the localization of the category of pairs of quasi-compact and quasi-separated schemes with an affine schematically dominant morphism between them localized with respect to simple relative blow ups and relative normalizations.