Rank one micro-locally free (epsilon)over-cap-modules and non-integrable connexions in dimension two

In [3], it is shown that above a complex manifold X of dimension greater th an or equal to 3, every micro-locally free E-module of rank 1 is of the for m <(<epsilon>)over cap> circle times (pi)-1 O pi L-1 for a line bundle L on X. This result is false in dimension 2, and the purpose of this Note is to determine the structure of the micro-locally free <(<epsilon>)over cap>- a nd D-modules of rank 1 in this case. One of the main result is the descript ion of micro-locally free D-modules of rank; 1 in terms of certain vector b undles on X with a non-integrable connexion. (C) 2001 Academie des sciences /Editions scientifiques et medicales Elsevier SAS.