Quadratic forms, division algebras and inseparable multiquadratic extensions. (Formes quadratiques, algèbres à division et extensions multiquadratiques inséparables.)
Quadratic forms over fields [Book]
Quadratic forms over fields with finite square class number
Quadratische Formen in beliebigen Körpern.
Quasi-additive functions.
Quelques remarques sur le -invariant
Realizing dyadic factors of elementary type Witt rings and pro-2 Galois groups.
Scaled trace forms of central simple algebras.
Similitude des multiples des formes d’Albert en caractéristique 2
Étant donnés un corps commutatif de caractéristique , des formes bilinéaires d’Albert et des -formes quadratiques de Pfister, ou des -formes bilinéaires de Pfister et des formes quadratiques d’Albert (resp. des formes bilinéaires d’Albert et des -formes bilinéaires de Pfister avec la condition que , , soient anisotropes), alors on montre que (resp.) si et seulement si est semblable à . Un exemple montre que la condition de l’anisotropie est nécessaire dans le cas bilinéaire....
Small zeros of quadratic forms over algebraic function fields
Some algebraic aspects of quadratic forms over fields of characteristic two.
Spectral Real Semigroups
The notion of a real semigroup was introduced in [8] to provide a framework for the investigation of the theory of (diagonal) quadratic forms over commutative, unitary, semi-real rings. In this paper we introduce and study an outstanding class of such structures, that we call spectral real semigroups (SRS). Our main results are: (i) The existence of a natural functorial duality between the category of SRSs and that of hereditarily normal spectral spaces; (ii) Characterization of the SRSs as the...
Splitting patterns of excellent quadratic forms.
Sums of powers in rings and the real holomorphy ring.
Symbol lengths in Milnor -theory.
Ten problems on quadratic forms
The image of the natural homomorphism of Witt rings of orders in a global field
Let R be a Dedekind domain whose field of fractions is a global field. Moreover, let 𝓞 < R be an order. We examine the image of the natural homomorphism φ : W𝓞 → WR of the corresponding Witt rings. We formulate necessary and sufficient conditions for the surjectivity of φ in the case of all nonreal quadratic number fields, all real quadratic number fields K such that -1 is a norm in the extension K/ℚ, and all quadratic function fields.
The intersection theorem for orderings of higher level in rings.
The Noether-Lefschetz theorem and sums of 4 squares in the rational function field
The quadratic form transfer and valuations.