A characterization of tame Hilbert-symbol equivalence
A characterization of the finite wild sets of rational self-equivalences
A Gersten–Witt spectral sequence for regular schemes
A note on the Hasse principle. Addenda
A purity theorem for the Witt group
A short proof of Rost nilpotence via refined correspondences.
Additive structure of multiplicative subgroups of fields and Galois theory.
An analogue of Pfister's local-global principle in the burnside ring
Let be a Galois extension with Galois group . We study the set of -linear combinations of characters in the Burnside ring which give rise to -linear combinations of trace forms of subextensions of which are trivial in the Witt ring W of . In particular, we prove that the torsion subgroup of coincides with the kernel of the total signature homomorphism.
An invariant of quadratic forms over schemes.
Annihilating polynomials for quadratic forms.
Arf equivalence II
Automorphisms of products of Witt rings of local type
Automorphisms of Witt rings of global fields
We construct an uncountable set of strong automorphisms of the Witt ring of a global field.
Biquaternion algebras and quartic extensions
Certain linear combinations of two Pfister forms and the isotropy problem. (Certaines combinaisons linéaires de deux formes de Pfister et le problème d'isotropie.)
Constructing Quasi-Pythagorean Fields
Dimensions of anisotropic indefinite quadratic forms. I.
Dimensions of anisotropic indefinite quadratic forms. II.
Divisible subgroups of Brauer groups and trace forms of central simple algebras.
Dualization in algebraic K-theory and the invariant e¹ of quadratic forms over schemes
In the classical Witt theory over a field F, the study of quadratic forms begins with two simple invariants: the dimension of a form modulo 2, called the dimension index and denoted e⁰: W(F) → ℤ/2, and the discriminant e¹ with values in k₁(F) = F*/F*², which behaves well on the fundamental ideal I(F)= ker(e⁰). Here a more sophisticated situation is considered, of quadratic forms over a scheme and, more generally, over an exact category with duality. Our purposes are: ...