Polars of Artin-Schreier curves
Poles of a local zeta function and Newton polygons
Poles of Igusa's local zeta function and monodromy
Poles of -adic complex powers and Newton polyhedra
Polyèdre caractéristique et éclatements combinatoires.
Polyèdre de Newton et distribution f... +. II.
Polyèdre de Newton et genre géométrique d'une singularité intersection complète
Polyèdre de Newton, éventails et désingularisation, d'après A. N. Varchenko
Polygone de Newton et théorème de préparation
Polygons with hidden vertices.
Polynôme d'Hilbert-Samuel des clôtures intégrales des puissances d'un idéal m-primaire
Polynômes de Bernstein associés à une fonction sur une intersection complète à singularité isolée
Nous montrons comment calculer des équations fonctionnelles du type de Bernstein associées à une fonction et aux sections du module de cohomologie locale algébrique à support une intersection complète quasi-homogène à singularité isolée.
Polynômes de Bernstein et monodromie
Polynômes de Bernstein-Sato associés à une intersection complète quasi-homogène à singularité isolée
Polynomial Automorphisms Over Finite Fields
It is shown that the invertible polynomial maps over a finite field Fq , if looked at as bijections Fn,q −→ Fn,q , give all possible bijections in the case q = 2, or q = p^r where p > 2. In the case q = 2^r where r > 1 it is shown that the tame subgroup of the invertible polynomial maps gives only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fn,q can be a zero set of a coordinate if and only if #S = q^(n−1).
Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group
2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.If F is a polynomial automorphism over a finite field Fq in dimension n, then it induces a permutation pqr(F) of (Fqr)n for every r О N*. We say that F can be “mimicked” by elements of a certain group of automorphisms G if there are gr О G such that pqr(gr) = pqr(F). Derksen’s theorem in characteristic zero states that the tame automorphisms in dimension n і 3 are generated by the affine maps and the one map (x1+x22, x2,ј, xn). We show...
Polynomial bounds for abelian groups of automorphisms
Polynomial bounds for the number of automorphisms of a surface of general type
Polynomial bounds for the oscillation of solutions of Fuchsian systems
We study the problem of placing effective upper bounds for the number of zeroes of solutions of Fuchsian systems on the Riemann sphere. The principal result is an explicit (non-uniform) upper bound, polynomially growing on the frontier of the class of Fuchsian systems of a given dimension having singular points. As a function of , this bound turns out to be double exponential in the precise sense explained in the paper.As a corollary, we obtain a solution of the so-called restricted infinitesimal...
Polynomial cycles in certain local domains
1. Let R be a domain and f ∈ R[X] a polynomial. A k-tuple of distinct elements of R is called a cycle of f if for i=0,1,...,k-2 and . The number k is called the length of the cycle. A tuple is a cycle in R if it is a cycle for some f ∈ R[X]. It has been shown in [1] that if R is the ring of all algebraic integers in a finite extension K of the rationals, then the possible lengths of cycles of R-polynomials are bounded by the number , depending only on the degree N of K. In this note we consider...