Hermitian forms over odd dimensional algebras

Hyperbolicity of Hermitian Forms over Biquaternion Algebras

We show that a non-hyperbolic hermitian form over a biquaternion algebra over a field of characteristic 6= 2 remains non-hyperbolic over a generic splitting field of the algebra.

Hermitian Forms over Ordered ∗-fields

Let D be a division ring with an involution. Assuming that D admits Baer orderings, we can study the Witt group of hermitian froms over D by observing its image in the ring of continuous functions on the space of orderings. We are led to define a new class of rings which, when viewed in an abstract setting, provide a natural generalization of the spaces of orderings and real spectra studied in ...

Orderings, Valuations and Hermitian Forms over ∗-fields

Binary Hermitian forms over a cyclotomic field

Article history: Received 21 January 2009 Available online 8 July 2009 Communicated by John Cremona

On hermitian trace forms over hilbertian fields

Let k be a field of characteristic different from 2. Let E/k be a finite separable extension with a k-linear involution σ. For every σ-symmetric element μ ∈ E∗, we define a hermitian scaled trace form by x ∈ E 7→ TrE/k(μxx). If μ = 1, it is called a hermitian trace form. In the following, we show that every even-dimensional quadratic form over a hilbertian field, which is not isomorphic to the ...