Résultats récents sur l'approximation des morphismes en algèbre commutative
Rigidity of Quotient Singularities.
Rings with approximation property.
Simple Singularities in Positive Characteristic.
Singularities Determined by Their Discriminant.
Some zero-dimensional generic singularities ; finite algebras having small tangent space
Sur la linéarité de la fonction de Artin
Sur les Plongements du Type Déformation.
The cohomology of Monsky and Washnitzer
The concept of (ν)-equivalence in algebraic deformation theory
The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity
Let X be a quotient surface singularity, and define as the directed graph of maximal Cohen-Macaulay (MCM) modules with edges corresponding to deformation incidences. We conjecture that the number of connected components of is equal to the order of the divisor class group of X, and when X is a rational double point (RDP), we observe that this follows from a result of A. Ishii. We view this as an enrichment of the McKay correspondence. For a general quotient singularity X, we prove the conjecture...
The embedding dimension of the formal Moduli space of certain curve singularities.
The graded Lie algebra of a Kähler group.
Théorèmes de préparation Gevrey et étude de certaines applications formelles
We consider subrings A of the ring of formal power series. They are defined by growth conditions on coefficients such as, for instance, Gevrey conditions. We prove preparation theorems of Malgrange type in these rings. As a consequence we study maps F from to without constant term such that the rank of the Jacobian matrix of F is equal to 1. Let be a formal power series. If F is a holomorphic map, the following result is well known: ∘ F is analytic implies there exists a convergent power series...
Travaux de Zink
The diverse Dieudonné theories have as their common goal the classification of formal groups and -divisible groups. The most recent theory is Zink’s theory of displays. A display over a ring R is a finitely generated projective module over the ring of Witt vectors, , equipped with additional structures. Zink has shown that using this notion, more concrete than those previously defined, one can obtain a good theory and prove an equivalence theorem in great generality. I will give an overview of...
Ultraproducts and Approximation in Local Rings I.
Ultraproducts and Approximation in Local Rings. II.
Une propriété de spécialisation continue
Which weakly ramified group actions admit a universal formal deformation?
Consider a representation of a finite group as automorphisms of a power series ring over a perfect field of positive characteristic. Let be the associated formal mixed-characteristic deformation functor. Assume that the action of is weakly ramified, i.e., the second ramification group is trivial. Example: for a group action on an ordinary curve, the action of a ramification group on the completed local ring of any point is weakly ramified.We prove that the only such that are not pro-representable...
Конечные модули Галуа