Espaces de Moisezon relatifs et algébrisation des modifications analytiques.
Formal deformation of curves with group scheme action
We study equivariant deformations of singular curves with an action of a finite flat group scheme, using a simplified version of Illusie's equivariant cotangent complex. We apply these methods in a special case which is relevant for the study of the stable reduction of three point covers.
Formale Geometrie und homogene Räume.
Géométrie des points épais
Infinitesimal deformations of complex surfaces with boundary.
Infinitesimal Deformations of Cusp Singularities.
Konvergenz formaler komplexer Räume mit konvexem oder konkavem Normalenbündel.
Lech inequalities for deformations of singularities defined by power products of degree 2.
Lifting -modules from positive to zero characteristic
We study liftings or deformations of -modules ( is the ring of differential operators from EGA IV) from positive characteristic to characteristic zero using ideas of Matzat and Berthelot’s theory of arithmetic -modules. We pay special attention to the growth of the differential Galois group of the liftings. We also apply formal deformation theory (following Schlessinger and Mazur) to analyze the space of all liftings of a given -module in positive characteristic. At the end we compare the problems...
Local moduli for plane curve singularities, the dimension of the ...-constant stratum.
Nonflat deformations of modules and isolated singularities.
On Certain Numbers Associated to Isolated Critical Points.
On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties
On the Module of Zariski Differentials and Infinitesimal Deformations of Cusp Singularities.
On Zariski's theorem in positive characteristic
In the current paper we show that the dimension of a family of irreducible reduced curves in a given ample linear system on a toric surface over an algebraically closed field is bounded from above by , where denotes a general curve in the family. This result generalizes a famous theorem of Zariski to the case of positive characteristic. We also explore new phenomena that occur in positive characteristic: We show that the equality does not imply the nodality of even if belongs to the...
-adic monodromy of the universal deformation of a HW-cyclic Barsotti-Tate group.
Potenzreihenerweiterung und formale Fasern in lokalen Ringen mit Approximationseigenschaft.
Power Series Solutions of Algebraic Differential Equations.
Projective modules and approximation couples
Propriété d'approximation pour les éléments algébriques