Linkage Property of Witt Ring and Torsion Quadratic Forms with Trivial Witt Invariant

Quadratic Forms over Fields Ii: Structure of the Witt Ring

The Chow-Witt ring

On the First Witt Index of Quadratic Forms

We prove Hoffmann’s conjecture determining the possible values of the first Witt index of anisotropic quadratic forms of any given dimension. The proof makes use of the Steenrod type operations on the modulo 2 Chow groups constructed by P. Brosnan. Let F be a field of characteristic 6= 2. For an anisotropic quadratic form φ over F with dim(φ) ≥ 2, the first Witt index i1(φ) is the Witt index (i...

Construction of the Ring of Witt Vectors

I will describe a functor A 7→ W (A) from the category of commutative rings to itself. The ring W (A) of ‘Witt vectors’ over A has many applications (to algebraic geometry, local rings, etc.), but I won’t discuss those. Convention: rings have 1’s that are respected by ring homomorphisms. By A I will always denote a commutative ring. The literature on the functor W is in a somewhat unsatisfactor...

The Reduced Witt Ring of a Formally

The reduced Witt rings of certain formally real fields are computed here in terms of some basic arithmetic invariants of the fields. For some fields, including the rational function field in one variable over the rational numbers and the rational function field in two variables over the real numbers, this is done by computing the image of the total signature map on the Witt ring. For a wider cl...