A class of symmetric biadditive functionals.
A classification of rank 6 quadratic spaces via pfaffians.
A family of symmetric biadditive nonbilinear functions.
A quantitative version of Hurwitz' theorem on the arithmetic-geometric inequality.
A question on the discriminants of involutions of central division algebras.
A Reciprocity Formula for Quadratic Forms.
A Recursive Description of the Maximal Pro-2 Galois Group Via Witt Rings.
A short proof of Rost nilpotence via refined correspondences.
Algebraic -theory and sums-of-squares formulas.
Algebraic systems of quadratic forms of number fields and function fields.
An alternative proof of Scheiderer's theorem on the Hasse principle for principal homogeneous spaces.
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.
Applied mathematics meets signal processing.
Around rationality of cycles
We prove certain results comparing rationality of algebraic cycles over the function field of a quadric and over the base field. These results have already been obtained by Alexander Vishik in the case of characteristic 0, which allowed him to work with algebraic cobordism theory. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2.
Birational geometry of quadrics
We construct new birational maps between quadrics over a field. The maps apply to several types of quadratic forms, including Pfister neighbors, neighbors of multiples of a Pfister form, and half-neighbors. One application is to determine which quadrics over a field are ruled (that is, birational to the projective line times some variety) in a larger range of dimensions. We describe ruledness completely for quadratic forms of odd dimension at most 17, even dimension at most 10, or dimension 14....
Certain linear combinations of two Pfister forms and the isotropy problem. (Certaines combinaisons linéaires de deux formes de Pfister et le problème d'isotropie.)
Classes de Stiefel-Whitney de Formes quadratiques et de représentations galoisiennes réelles.
Classification of hermitian forms and semisimple gorups over fields of virtual cohomological dimension one.
Cyclotomic equations and square properties in rings.
Definite Lattices Over Real Algebraic Function Domains.