2010/10/26 by Janós Kollár, János Kollár, Kollár, János
Mathematics · #12D10 #13A15 #14F05 #26C10 #54C05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #math.AG #msc:12D10 #msc:13A15 #msc:14F05 #msc:26C10 #msc:54C05
paper · pdf · doi:10.48550/arxiv.1010.5480
arxiv created 2010/10/26 · openalex publication_date 2010/10/26 · arxiv updated 2010/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a purely algebraic construction of the continuous closure of any finitely generated torsion free module; a concept first studied by H.~Brenner and M.~Hochster. The construction implies that, at least in characteristic 0, taking continuous closure commutes with flat morphisms whose fibers are semi-normal. This implies that the continuous closure of a coherent ideal sheaf is again a coherent ideal sheaf (both in the Zariski and in the étale topologies) and it commutes with field extensions.