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.