2008/01/28 by Daniel Barlet, Barlet, Daniel
Mathematics · #32S05 #32S20 #32S25 #32S40 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Rings, Modules, and Algebras #math.AG #math.CV #msc:32S05 #msc:32S20 #msc:32S25 #msc:32S40
paper · pdf · doi:10.48550/arxiv.0801.4320
arxiv created 2008/01/28 · openalex publication_date 2008/01/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove the following two results 1. For a proper holomorphic function f : X → D of a complex manifold X on a disc such that \df = 0 \ ⊂ f-1(0), we construct, in a functorial way, for each integer p, a geometric (a,b)-module Ep associated to the (filtered) Gauss-Manin connexion of f. This first theorem is an existence/finiteness result which shows that geometric (a,b)-modules may be used in global situations. 2. For any regular (a,b)-module E we give an integer N(E), explicitely given from simple invariants of E, such that the isomorphism class of E/bN(E).E determines the isomorphism class of E. This second result allows to cut asymptotic expansions (in powers of b) of elements of E without loosing any information.