Local cohomology of sheaves of differential forms and Hodge theory.
Logarithmic differential operators and logarithmic de Rham complexes relative to a free divisor
Modules des differentielles en caracteristique p.
...-Modules on Supermanifolds.
Moduli of pre-...-modules, preverse sheaves and the Riemann-Hilbert morphism. I.
Nicht-ausgeartete reguläre Überlagerungen.
Nonabelian Hodge theory in characteristic
Given a scheme in characteristic p together with a lifting modulo p2, we construct a functor from a category of suitably nilpotent modules with connection to the category of Higgs modules. We use this functor to generalize the decomposition theorem of Deligne-Illusie to the case of de Rham cohomology with coefficients.
On a generalization of Hilbert's 21st problem
On a question of Demailly-Peternell-Schneider
We give an affirmative answer to an open question posed by Demailly-Peternell-Schneider in 2001 and recently by Peternell. Let be a surjective morphism from a log canonical pair onto a -Gorenstein variety . If is nef, we show that is pseudo-effective.
On Almost Complete Intersections.
On Barth's restriction theorem.
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 relative canonical sheaves of arithmetic surfaces.
On the cohomology of a general fiber of a polynomial map
On the de Rham cohomology of algebraic varieties
On the Module of Zariski Differentials and Infinitesimal Deformations of Cusp Singularities.
On the Normal Bundle of Curves on Complete Intersection Surfaces.
On the Spannedness and Very Ampleness of Certain Line Bundles on the Blow-ups of IP2C and Fr .