Courbes définies sur les corps de séries formelles et loi de réciprocité (Acta Arithmetica 42 (1982), p. 101-106) (Errata)
Courbes définies sur les corps de séries formelles et loi de réciprocité
Cyclically valued rings and formal power series
Rings of formal power series with exponents in a cyclically ordered group were defined in [2]. Now, there exists a “valuation” on : for every in and in , we let be the first element of the support of which is greater than or equal to . Structures with such a valuation can be called cyclically valued rings. Others examples of cyclically valued rings are obtained by “twisting” the multiplication in . We prove that a cyclically valued ring is a subring of a power series ring with...
Décomposition cellulaire de variétés paramétrant des idéaux homogènes de C [[x,y]]. Incidence des cellules - II -.
Deformation von Cohen-Macaulay Algebren.
Degree estimate for subalgebras generated by two elements
We develop a new combinatorial method to deal with a degree estimate for subalgebras generated by two elements in different environments. We obtain a lower bound for the degree of the elements in two-generated subalgebras of a free associative algebra over a field of zero characteristic. We also reproduce a somewhat refined degree estimate of Shestakov and Umirbaev for the polynomial algebra, which plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong...
Der Hauptsatz über Iteration im Ring der formalen Potenzreihen.
Der Residuenkomplex in der lokalen algebraischen und analytischen Geometrie.
Diagonales de fractions rationnelles et équations de Picard-Fuchs
Diagonalization and rationalization of algebraic Laurent series
We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime the reduction modulo of the diagonal of a multivariate algebraic power series with integer coefficients is an algebraic power series of degree at most and height at most , where is an effective constant that only depends on...
Division dans l'anneau des séries formelles à croissance contrôlée. Applications
We consider subrings A of the ring of formal power series. They are defined by growth conditions on coefficients such as, for instance, Gevrey conditions. We prove a Weierstrass-Hironaka division theorem for such subrings. Moreover, given an ideal ℐ of A and a series f in A we prove the existence in A of a unique remainder r modulo ℐ. As a consequence, we get a new proof of the noetherianity of A.
Efficient generation of zero dimensional ideals in polynomial rings.
Eindimensionale fast-vollständige Durchschnitte sind nicht starr.
Éléments algébriques remarquables dans un corps de séries formelles
Equations in the Hadamard ring of rational functions
Let be a number field. It is well known that the set of recurrencesequences with entries in is closed under component-wise operations, and so it can be equipped with a ring structure. We try to understand the structure of this ring, in particular to understand which algebraic equations have a solution in the ring. For the case of cyclic equations a conjecture due to Pisot states the following: assume is a recurrence sequence and suppose that all the have a root in the field ; then (after...
Errata to the paper "Remarks of the elementary theories of formal and convergent power series" Fundamenta Mathematicae 105 (1980), pp. 229-239
Extending Meromorphic Functions on a Grassmannian Variety.
Factorisation de Ritt pour les polynômes exponentiels formels
Factorisation de suites récurrentes linéaires
Filtrations by complete ideals and applications.