2015/11/19 by Fernando Sancho de Salas, de Salas, Fernando Sancho
Mathematics · #05-XX #06-XX #14-XX #55PXX #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:05-XX #msc:06-XX #msc:14-XX #msc:55PXX
paper · pdf · doi:10.48550/arxiv.1511.06284
15 pages. arXiv admin note: substantial text overlap with arXiv:1409.4574
arxiv created 2015/11/19 · openalex publication_date 2015/11/19 · arxiv updated 2015/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed space, endowed with a finite open covering, produces a ringed finite space. We study the homotopy of ringed finite spaces, extending Stong's homotopy classification of finite topological spaces to ringed finite spaces. We also prove that the category of quasi-coherent modules on a ringed finite space is a homotopy invariant.