Modules simples sur une algèbre de Lie nilpotente contenant un vecteur propre pour une sous-algèbre
Moduli of pre-...-modules, preverse sheaves and the Riemann-Hilbert morphism. I.
Necessary and sufficient conditions for the local solvability in hyperfunctions of a class of systems of complex vector fields.
On Deligne-Malgrange lattices, resolution of turning points and harmonic bundles
In this short survey, we would like to overview the recent development of the study on Deligne-Malgrange lattices and resolution of turning points for algebraic meromorphic flat bundles. We also explain their relation with wild harmonic bundles. The author hopes that it would be helpful for access to his work on wild harmonic bundles.
On direct and inverse images of D-Modules in prime characteristic.
On meromorphic functions defined by a differential system of order
Given a germ of holomorphic function on , we study the condition: “the ideal is generated by operators of order1”. We obtain here full characterizations in the particular cases of Koszul-free germs and unreduced germs of plane curves. Moreover, we prove that this condition holds for a special type of hyperplane arrangements. These results allow us to link this condition to the comparison of de Rham complexes associated with .
On microlocal -function
On non-holonomic irreducible D-modules.
On the cohomology of a general fiber of a polynomial map
On the dual space of the Tjurina algebra attached to a semi-quasihomogeneous isolated singularity
A dual space of the Tjurina algebra attached to a non-quasihomogeneous unimodal or bimodal singularity is considered. It is shown that almost every algebraic local cohomology class, belonging to the dual space, can be characterized as a solution of a holonomic system of first order differential equations.
On the Homological Dimension of a Der-Free Hypersurface.
One-dimensional infinitesimal-birational duality through differential operators
The structure of filtered algebras of Grothendieck's differential operators on a smooth fat point in a curve and graded Poisson algebras of their principal symbols is explicitly determined. A related infinitesimal-birational duality realized by a Springer type resolution of singularities and the Fourier transformation is presented. This algebro-geometrical duality is quantized in appropriate sense and its quantum origin is explained.
Polynômes de Bernstein associés à une fonction sur une intersection complète à singularité isolée
Nous montrons comment calculer des équations fonctionnelles du type de Bernstein associées à une fonction et aux sections du module de cohomologie locale algébrique à support une intersection complète quasi-homogène à singularité isolée.
Polynômes de Bernstein-Sato associés à une intersection complète quasi-homogène à singularité isolée
Positivité de l’irrégularité des -modules
Principe de Boyarsky et ...-modules.
Problème de Cauchy ramifié en théorie des faisceaux (d'après un travail avec P. Schapira)
Proximité évanescente. I. La structure polaire d’un -module
Proximité évanescente. II. Équations fonctionnelles pour plusieurs fonctions analytiques
Quotient spaces and critical points of invariant functions for C*-actions.