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Formes quadratiques et extensions en caractéristique 2

Anne-Marie Bergé, Jacques Martinet (1985)

Annales de l'institut Fourier

On associe à toute extension finie E d’un corps K de caractéristique 2 une forme quadratique non dégénérée de rang pair égal à [ E : K ] [ E : K ] + 1 , dont on détermine les invariants. On applique ensuite cette étude à la recherche de polynômes dépendant de peu de paramètres permettant de définir des familles d’extensions de degré donné.

Grothendieck and Witt groups in the reduced theory of quadratic forms

Andrzej Sładek (1980)

Annales Polonici Mathematici

Abstract. Let F be a formally real field. Denote by G(F) and G t ( F ) the Grothen-dieck group of quadratic forms over F and its torsion subgroup, respectively. In this paper we study the structure of the factor group G ( F ) / G t ( F ) . This reduced Grothendieck group is a free Abelian group. The main results of the paper describe some sets of generators for G ( F ) / G t ( F ) , which in many cases allow us to find a basis for the group. Throughout the paper we use the language of the reduced theory of quadratic forms. In the final part...

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