2023/05/30 by Federico Bongiorno, Bongiorno, Federico · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2305.18813
openalex publication_date 2023/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this article is to give a rigorous geometric interpretation of the completion of a ring with respect to an ideal. To this end, we define the infinitesimal neighbourhood of an immersion of formal schemes as the largest possible thickening. Further, we show that immersions of formal schemes locally of formal finite presentation admit the existence of infinitesimal neighbourhoods, which are locally given by completing with respect to an ideal.