Two finiteness theorem for $(a,b)$-module
  We prove the following two results   1. For a proper holomorphic function $ f : X \to D$ of a complex manifold   $X$ on a disc such that $\{df = 0 \} \subset f^{-1}(0)$, we construct, in a functorial way, for each integer $p$, a geometric (a,b)-module $E^p$ \ 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 $E\big/b^{N(E)}.E$ 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. 
Daniel Barlet