A note on the one-dimensional systems of formal equations
On this paper we compute the numerical function of the approximation theorem of M. Artin for the one-dimensional systems of formal equations.
Approximation diophantienne dans les corps de séries en plusieurs variables
Nous montrons ici un théorème d’approximation diophantienne entre le corps des séries formelles en plusieurs variables et son complété pour la topologie de Krull.
Deforming syzygies of liftable modules and generalised Knörrer functors
Maps between deformation functors of modules are given which generalise the maps induced by the Knörrer functors. These maps become isomorphisms after introducing certain equations in the target functor restricting the Zariski tangent space. Explicit examples are given on how the isomorphisms extend results about deformation theory and classification of MCM modules to higher dimensions.
Generalized ring of norms and generalized -modules
Images directes I : Espaces rigides analytiques et images directes
Cet article est le premier d’une série de trois articles consacrés aux images directes d’isocristaux : ici nous considérons des isocristaux sans structure de Frobenius ; dans le deuxième [Et 6] (resp. le troisième [Et 7]), nous introduirons une structure de Frobenius dans le contexte convergent (resp. surconvergent).Pour un morphisme propre et lisse relevable nous établissons la surconvergence des images directes, grâce à un théorème de changement de base pour un morphisme propre entre espaces rigides...
Non-existence of the Artin function for Henselian pairs.
On Strong Going-Between, Going-Down, And Their Universalizations, II
We consider analogies between the logically independent properties of strong going-between (SGB) and going-down (GD), as well as analogies between the universalizations of these properties. Transfer results are obtained for the (universally) SGB property relative to pullbacks and Nagata ring constructions. It is shown that if are domains such that is an LFD universally going-down domain and is algebraic over , then the inclusion map satisfies GB for each . However, for any nonzero ring...
On valuation spectra
Projective modules and approximation couples
Regularity and intersections of bracket powers
Among reduced Noetherian prime characteristic commutative rings, we prove that a regular ring is precisely that where the finite intersection of ideals commutes with taking bracket powers. However, reducedness is essential for this equivalence. Connections are made with Ohm-Rush content theory, intersection-flatness of the Frobenius map, and various flatness criteria.
Relèvements de schémas et algèbres de Monsky-Washnitzer : théorèmes d équivalence et de pleine fidélité II
Remarks on Henselian rings.
Résultats récents sur l'approximation des morphismes en algèbre commutative
Rings with approximation property.
Submersions and effective descent of étale morphisms
Using the flatification by blow-up result of Raynaud and Gruson, we obtain new results for submersive and subtrusive morphisms. We show that universally subtrusive morphisms, and in particular universally open morphisms, are morphisms of effective descent for the fibered category of étale morphisms. Our results extend and supplement previous treatments on submersive morphisms by Grothendieck, Picavet and Voevodsky. Applications include the universality of geometric quotients and the elimination...
The Artin conjecture for Q-algebras.
We give a simplification, in the case of Q-algebras, of the proof of Artin's Conjecture, which says that a regular morphism between Noetherian rings is the inductive limit of smooth morphisms of finite type.
Twisted forms of finite étale extensions and separable polynomials.
Un foncteur norme
Кольца с дискретной группой классов дивизоров