Quaternionic skew-hermitian forms over a number field

Cohomological Invariants of Quaternionic Skew-hermitian Forms

We define a complete system of invariants en,Q, n ≥ 0 for quaternionic skew-hermitian forms, which are twisted versions of the invariants en for quadratic forms. We also show that quaternionic skew-hermitian forms defined over a field of 2-cohomological dimension at most 3 are classified by rank, discriminant, Clifford invariant and Rost invariant.

Binary Hermitian forms over a cyclotomic field

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

Vector valued hermitian and quaternionic modular forms

∗-Valuations and Hermitian Forms on Skew Fields

This paper is a survey of the literature on ways in which the concept of ordering can be extended to the setting of a division ring with involution and the main results for these extensions.

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 ...