2024/01/04 by Phùng Hô Hái, Hai, Phùng Hô, Hop D. Nguyen +3
Mathematics · #13C11 #14L15 #14L17 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2401.02006
openalex publication_date 2024/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A very useful result concerning flatness in Algebraic Geometry is EGA's ``fiber'' criterion. We propose similar fiber criteria to verify flatness of a module while avoiding ``finiteness'' assumptions. Motivated by a Tannakian viewpoint (where the category of representations comes to the front), we derive applications to the theory of affine and flat group schemes.