2012/03/22 by Satoshi Takagi, Takagi, Satoshi
Mathematics · #11G99 #14A15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.AG #math.NT #msc:11G99 #msc:14A15
paper · pdf · doi:10.48550/arxiv.1203.4914
29 pages, 1 figure
openalex publication_date 2012/03/22 · arxiv created 2012/03/23 · arxiv updated 2012/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce a new algebraic type of `convexoid rings', and we give the definition of (weak) convexoid schemes, which share similar properties with ordinary schemes. As a result, we give a purely-algebraic construction of the compactification of Spec Z (in Arakelov's sense) which is realized as the Zariski-Riemann space in the category of weak convexoid schemes.