Fonctions -lipschitziennes sur un anneau local et polynômes à valeurs entières
Fonctions pseudo-concaves et anneaux henséliens
Formal deformation of curves with group scheme action
We study equivariant deformations of singular curves with an action of a finite flat group scheme, using a simplified version of Illusie's equivariant cotangent complex. We apply these methods in a special case which is relevant for the study of the stable reduction of three point covers.
Formal power series rings over a -domain
Formal prime ideals of infinite value and their algebraic resolution
Suppose that is a local domain essentially of finite type over a field of characteristic , and a valuation of the quotient field of which dominates . The rank of such a valuation often increases upon extending the valuation to a valuation dominating , the completion of . When the rank of is , Cutkosky and Ghezzi handle this phenomenon by resolving the prime ideal of infinite value, but give an example showing that when the rank is greater than , there is no natural ideal in that...
Formal relations between quasianalytic functions of some fixed class
In [Ga] Gabrielov has given conditions under which the completion of the kernel of a morphism φ: A → B between analytic rings coincides with the kernel of the induced morphism φ̂: Â → B̂ between the completions. If B is a domain, a sufficient condition is that rk φ = dim(Â/ker φ̂), where rk φ is the rank of the jacobian matrix of φ considered as a matrix over the quotient field of B. We prove that the above property holds in a fixed quasianalytic Denjoy-Carleman class if and only if the class coincides...
Formes d'inertie et complexe de Koszul associés à des polynômes plurihomogènes.
The existence of common zero of a family of polynomials has led to the study of inertial forms, whose homogeneous part of degree 0 constitutes the ideal resultant. The Kozsul and Cech cohomologies groups play a fundamental role in this study. An analogueous of Hurwitz theorem is given, and also, one finds a N. H. McCoy theorem in a particular case of this study.
Formes quadratiques sur les anneaux semi-locaux réguliers
Forms and mappings. I: Generalities
Forms Derived from the Arithmetic-Geometric Inequality.
Formules explicites intervenant dans la division euclidienne des polynômes à coefficients dans un anneau unitaire et applications diverses
Fortsetzung von Spezialisierungen: ein idealtheoretischer Zugang
Fractions rationnelles à valeurs entières
Fragmented deformations of primitive multiple curves
A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that Y red is smooth. We study the deformations of Y to curves with smooth irreducible components, when the number of components is maximal (it is then the multiplicity n of Y). We are particularly interested in deformations to n disjoint smooth irreducible components, which are called fragmented deformations. We describe them completely. We give also a characterization...
Fragmented integral domains
Fragments of almost ring theory
Fréchet algebras, formal power series, and automatic continuity
We describe all those commutative Fréchet algebras which may be continuously embedded in the algebra ℂ[[X]] in such a way that they contain the polynomials. It is shown that these algebras (except ℂ[[X]] itself) always satisfy a certain equicontinuity condition due to Loy. Using this result, some applications to the theory of automatic continuity are given; in particular, the uniqueness of the Fréchet algebra topology for such algebras is established.
Fréchet algebras of power series
We consider Fréchet algebras which are subalgebras of the algebra 𝔉 = ℂ [[X]] of formal power series in one variable and of 𝔉ₙ = ℂ [[X₁,..., Xₙ]] of formal power series in n variables, where n ∈ ℕ. In each case, these algebras are taken with the topology of coordinatewise convergence. We begin with some basic definitions about Fréchet algebras, (F)-algebras, and other topological algebras, and recall some of their properties; we discuss Michael's problem from 1952 on the continuity of characters...
Fredholm spectrum and growth of cohomology groups
Let T ∈ L(E)ⁿ be a commuting tuple of bounded linear operators on a complex Banach space E and let be the non-essential spectrum of T. We show that, for each connected component M of the manifold of all smooth points of , there is a number p ∈ 0, ..., n such that, for each point z ∈ M, the dimensions of the cohomology groups grow at least like the sequence with d = dim M.
Free minimal resolutions and the Betti numbers of the suspension of an -gon.