Over a global field any finite number of central simple algebras of exponent dividing m is split by a common cyclic field extension of degree m. We show that the same property holds for function fields of 2-dimensional ...

For quadratic forms in 4 variables defined over the rational function field in one variable over C((t)), the validity of the local-global principle for isotropy with respect to different sets of discrete valuations is examined.

For m >= 2, we study derivations on symbol algebras of degree m over fields with characteristic not dividing m. A differential central simple algebra over a field k is split by a finitely generated extension of k. For ...