2023/05/19 by J. Sánchez Gonzalez, González, Javier Sánchez
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2305.11693
openalex publication_date 2023/05/19 · openalex created_date 2023/05/23 · openalex updated_date 2026/07/28
We introduce a notion of proper morphism for schematic finite spaces and prove the analogue of Grothendieck's finiteness theorem for it by means of the classic result for schemes and general descent arguments. This result also generalizes the class of morphisms of schemes for which the conclusion of the aforementioned Theorem holds. The key is giving a weaker definition of locally finitely presented morphisms.