Partial Henselizations.
Permanenza di proprietà nella henselizzazione degli anelli non noetheriani
Points rationnels et méthode de Chabauty elliptique
La méthode de Chabauty elliptique permet de calculer les points rationnels sur une courbe définie sur un corps de nombres lorsque le théorème de Chabauty ne s’applique pas, c’est à dire lorsque le rang de la jacobienne est supérieur au genre de la courbe. Nous exposons cette méthode et nous la généralisons dans de nouveaux cas en écrivant une version explicite du théorème de préparation de Weierstrass en variables. En particulier nous calculons tous les points rationnels d’une courbe de genre...
Pointwise convergence fails to be strict
It is known that the ring of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of . In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of which differs from .
Positive polynomials and hyperdeterminants
Let F be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semi-definite. In this note we produce a necessary condition for positivity, and a sufficient condition for non-negativity, in terms of positivity or semi-positivity of a one-variable characteristic polynomial of F. Also, we revisit the known sufficient condition in terms of Hankel matrices.
Positive polynomials and polynomial inequalities.
Potenzreihenerweiterung und formale Fasern in lokalen Ringen mit Approximationseigenschaft.
Power Series over Coherent Rings.
Power Series Solutions of Algebraic Differential Equations.
p-Ranks of Class Groups in Zdp-Extensions.
Projective modules and approximation couples
Projectivity of pure ideals
Propriété d'approximation pour les éléments algébriques
Puiseux Expansion for Space Curves.