Isotropy of quadratic spaces in finite and infinite dimension.
Knebusch-Milnor exact sequence and parity of class numbers
L'invariant de Witt de la forme Tr(x2).
Local-global principle for Witt equivalence of function fields over global fields
We examine the conditions for two algebraic function fields over global fields to be Witt equivalent. We develop a criterion solving the problem which is analogous to the local-global principle for Witt equivalence of global fields obtained by R. Perlis, K. Szymiczek, P. E. Conner and R. Litherland [12]. Subsequently, we derive some immediate consequences of this result. In particular we show that Witt equivalence of algebraic function fields (that have rational places) over global fields implies...
L'octogone régulier et la signature des formes quadratiques entières non singulières
La formule généralisant la loi de réciprocité quadratique de Legendre et exprimant le reste par huit de la signature d'une forme quadratique entière non dégénérée à l'aide d'une somme de Gauss est attribuée par Milnor à Milgram, la faisant remonter à Braun. Le formalisme de Witt la réduit au cas de dimension 1 que Chandrasekharan attribue à Cauchy et Kronecker. Braun soulignait que les preuves de ces formules nécessitent des moyens d'analyse. Une propriété métrique de l'octogone...
Matching local Witt invariants
The starting point of this note is the observation that the local condition used in the notion of a Hilbert-symbol equivalence and a quaternion-symbol equivalence — once it is expressed in terms of the Witt invariant — admits a natural generalisation. In this paper we show that for global function fields as well as the formally real function fields over a real closed field all the resulting equivalences coincide.
Matching Witts locally and globally
Minimal forms with respect to function fields of conics.
Monoids of linking pairings and orthogonal summands. (Monoide des enlacements et facteurs orthogonaux.)
Motivic equivalence of quadratic forms.
Natural homomorphisms of Witt rings of orders in algebraic number fields. II
We prove that there are infinitely many real quadratic number fields with the property that for infinitely many orders in and for the maximal order in the natural homomorphism of Witt rings is surjective.
Natural homomorphisms of Witt rings of orders in algebraic number fields
Non unimodular Hermitian forms.
On 14-dimensional quadratic forms in , 8-dimensional forms in , and the common value property.
On a conjecture of Izhboldin on similarity of quadratic forms.
On existence of tame Harrison map
On integral Witt equivalence of algebraic number fields
On near-neighbor quadratic forms. (Autour des formes quadratiques quasi-voisines.)
On quadratic forms of height 3 and degree . (Sur les formes quadratiques de hauteur 3 et de degré au plus 2.)
On Real Local-Global Principles.