Solutions d'équations à coefficients dans un anneau hensélien
Some invariant theory among quasi-projectives
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...
Sur la compacité du spectre minimal d'un anneau
Tangent star cones.
Technique de descente et théorèmes d'existence en géométrie algébriques. II. Le théorème d'existence en théorie formelle des modules
The homotopy axiom in semialgebraic cohomology.
The set of points at which a morphism of affine schemes is not finite
Assume that X,Y are integral noetherian affine schemes. Let f:X → Y be a dominant, generically finite morphism of finite type. We show that the set of points at which the morphism f is not finite is either empty or a hypersurface. An example is given to show that this is no longer true in the non-noetherian case.
The spectrum associated to a radical operation.
The Spectrum of Equivariant K-theory.
The topological nature of algebraic contractions
The Witt Group of a Smooth Complex Surface.
Towards a theory of arithmetic degrees.
Universal covering spaces and fundamental groups in algebraic geometry as schemes
In topology, the notions of the fundamental group and the universal cover are closely intertwined. By importing usual notions from topology into the algebraic and arithmetic setting, we construct a fundamental group family from a universal cover, both of which are schemes. A geometric fiber of the fundamental group family (as a topological group) is canonically the étale fundamental group. The constructions apply to all connected quasicompact quasiseparated schemes. With different methods and hypotheses,...
Universal Weil Divisors.
Weierstrass points on schemes.
Zur Konstantenreduktion projektiver Schemata.
Zur Transitivität der normalen Flachheit.
Морфизм, разделяющий неконгруентные точки параметризирующей предсхемы плоского семейства подпредсхем. II
Морфизм, разделяющий неконгруентные точки параметризующей предсхемы плоского семейства подпредсхем. I