Effective Nullstellensatz and geometric degree for zero-dimensional ideals
Effective Nullstellensatz for arbitrary ideals
Let be polynomials in variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials such that . The effective versions of this result bound the degrees of the in terms of the degrees of the . The aim of this paper is to generalize this to the case when the are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed.
Ein Beweis des Hilbertschen Basissatzes.
Ein Semialgebraischer Beweis der Topologischen Form des Hauptsatzes von zariski.
Eine Anwendung des Selbergschen Siebes auf algebraische Zahlkörper
Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes.
Equations de variétés de Kummer.
Errata et addenda à «Lemmes de zéros dans les groupes algébriques commutatifs»
Every Algebraic Set in n-Space Is the Intersection of n Hypersurfaces.
Exposé on a conjecture of Tougeron
An algebra homomorphism of the locatized affine rings of an algebraic variety is continuous in the Krull topology of the respective local rings. It is not necessarily open or closed in the Krull topology. However, we show that the induced map on the associated analytic local rings is also open and closed in the Krull topology. To do this we prove a conjecture of Tougeron which states that if is an analytic curve on an analytic variety and is a formal power series which is convergent when restricted...