Ein Residuensatz für symmetrische Bilinearformen.
Ein Satz über die Werte von quadratischen Formen über Körper.
Erratum. Quelques remarques sur le -invariant
Excellent special orthogonal groups.
Faithfully quadratic rings - a summary of results
This is a summary of some of the main results in the monograph Faithfully Ordered Rings (Mem. Amer. Math. Soc. 2015), presented by the first author at the ALANT conference, Będlewo, Poland, June 8-13, 2014. The notions involved and the results are stated in detail, the techniques employed briefly outlined, but proofs are omitted. We focus on those aspects of the cited monograph concerning (diagonal) quadratic forms over preordered rings.
Finiteness theorems for forms over global fields.
Formally real fields, pythagorean fields, C-fields and W-groups.
Formes quadratiques et cycles algébriques
Introduite par Witt en 1937, la théorie des formes quadratiques sur un corps joue un rôle central dans la démonstration des conjectures de Milnor par Voevodsky via les travaux pionniers de Rost qui y interviennent. Réciproquement, les méthodes de Rost et Voevodsky utilisant la théorie des motifs et les opérations de Steenrod motiviques révolutionnent la théorie des formes quadratiques et ont conduit à la démonstration de résultats de base qui semblaient auparavant inaccessibles. On expliquera notamment...
Function Fields of Quadratic Forms.
Galois cohomology of biquadratic extensions.
Generalized Hubert fields, II
Geometric description of the connecting homomorphism for Witt groups.
Graded quaternion symbol equivalence of function fields
We present criteria for a pair of maps to constitute a quaternion-symbol equivalence (or a Hilbert-symbol equivalence if we deal with global function fields) expressed in terms of vanishing of the Clifford invariant. In principle, we prove that a local condition of a quaternion-symbol equivalence can be transcribed from the Brauer group to the Brauer-Wall group.
Hilbert-symbol equivalence of global function fields
Holes in
Invariants of a quadratic form attached to a tame covering of schemes
We build on preceeding work of Serre, Esnault-Kahn-Viehweg and Kahn to establish a relation between invariants, in modulo 2 étale cohomology, attached to a tamely ramified covering of schemes with odd ramification indices. The first type of invariant is constructed using a natural quadratic form obtained from the covering. In the case of an extension of Dedekind domains, mains, this form is the square root of the inverse different equipped with the trace form. In the case of a covering of Riemann...
Involutions and trace forms on exterior powers of a central simple algebra.
Isotropy and factorization in reduced Witt rings.
Isotropy of quadratic forms over function fields of -adic curves
Isotropy of quadratic forms over the function field of a quadric.