Function Fileds of Pfister Forms.
Generalized Hilbert fields.
Generating functions of finitely generated Witt rings
Geometry of normed bilinear maps and the 16-square problem.
G-invariant quadratic forms.
Gitter ohne Automorphismen der Determinante.
Graded Witt Rings of Elementary Type.
Grothendieck and Witt groups in the reduced theory of quadratic forms
Abstract. Let F be a formally real field. Denote by G(F) and 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 . This reduced Grothendieck group is a free Abelian group. The main results of the paper describe some sets of generators for , 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...
Higher Level Reduced Witt Rings of Skew Fields.
Holes in
Homomorphisms of Unitary Groups.
Hyperbolic involutions.
Inertial law of quadratic forms on modules over plural algebra
Quadratic forms on a free finite-dimensional module are investigated. It is shown that the inertial law can be suitably generalized provided the vector space is replaced by a free finite-dimensional module over a certain linear algebra over ( real plural algebra) introduced in [1].
Isometries of quadratic spaces
Let be a global field of characteristic not 2, and let be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial if and only if such an isometry exists over all the completions of . This gives a partial answer to a question of Milnor.
Isotropy of quadratic forms over function fields of -adic curves
Isotropy of quadratic forms over the function field of a quadric.
Isotropy of quadratic spaces in finite and infinite dimension.
Kronecker modules and reductions of a pair of bilinear forms
We give a short overview on the subject of canonical reduction of a pair of bilinear forms, each being symmetric or alternating, making use of the classification of pairs of linear mappings between vector spaces given by J. Dieudonné.
La controverse de 1874 entre Camille Jordan et Leopold Kronecker
Une vive querelle oppose en 1874 Camille Jordan et Leopold Kronecker sur l’organisation de la théorie des formes bilinéaires, considérée comme permettant un traitement « général » et « homogène » de nombreuses questions développées dans des cadres théoriques variés au xixe siècle et dont le problème principal est reconnu comme susceptible d’être résolu par deux théorèmes énoncés indépendamment par Jordan et Weierstrass. Cette controverse, suscitée par la rencontre de deux théorèmes que nous considérerions...
L'invariant de Witt de la forme Tr(x2).