No abstract

Using the calculation of the resulting of polynomials, we describe in this paper a new method to prove the stability of a polynomial f (x) of second degree, that is the irreducibility of all the iterates of f . Mathematics Subject Classification: 11R09, 11T06, 12E10

Consider an algebraic number field K of degree n, A K is its ring of integers and a prime number p inert in K. Let F (u 1 , . . . , u n , x) be the generic polynomial of integers of K. We will study in advance the stability of this polynomial and then, we will apply it in order to obtain all the monic irreducible polynomials in F p [x] of degree d dividing n.Mathematics Subject Classification: 11R09, 11T06, 12E10

In this paper, we calculate the Witt groups of smooth projective toric surfaces over a field of characteristic different from 2. Such a surface is described combinatorially by a fan in the plan. The result is a direct sum of several copies of the Witt group of the basic field, their number depends on the line bundle used in the definition of Witt groups. The technique of the proofs is to filter the derived category of the surface by subcategories with support in unions of orbits closures whose dimension is 1. Then, by excision, we obtain long exact sequences including copies of Witt groups of the basic field.