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Birational Spaces

2013/11/27 by Uri Brezner, Brezner, Uri
Mathematics · #Advanced Operator Algebra Research #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.1311.6919

openalex publication_date 2013/11/27 · arxiv created 2013/11/28 · arxiv updated 2013/12/02 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this paper we construct the category of birational spaces as the category in which Temkin's relative Riemann-Zariski spaces 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 relative blow ups and relative normalizations.

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