2006/04/11 by Alonso, Leovigildo, Jeremias, Ana, Marta Pérez +1 · 1 citation
Mathematics · #14B25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 14B10 #Secondary 14B20
paper · pdf · doi:10.48550/arxiv.math/0604241
openalex publication_date 2006/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This a first step to develop a theory of smooth, etale and unramified morphisms between noetherian formal schemes. Our main tool is the complete module of differentials, that is a coherent sheaf whenever the map of formal schemes is of pseudo finite type. Among our results we show that these infinitesimal properties of a map of usual schemes carry over into the completion with respect to suitable closed subsets. We characterize unramifiedness by the vanishing of the module of differentials. Also we see that a smooth morphism of noetherian formal schemes is flat and its module of differentials is locally free. The paper closes with a version of Zariski's Jacobian criterion.