A Gersten–Witt spectral sequence for regular schemes
A purity theorem for the Witt group
Algebraic K-Theory and Quadratic Forms.
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: ...
Function Fields of Quadratic Forms.
Geometric description of the connecting homomorphism for Witt groups.
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
On the Witt rings of function fields of quasihomogeneous varieties
Picard groups of Witt rings.
Symplectic K2 of Laurent polynomials, associated Kac-Moody groups and Witt rings.
The Gersten conjecture for Witt groups in the equicharacteristic case.
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.
Witt group of Hermitian forms over a noncommutative discrete valuation ring.
Witt groups of projective line bundles.