Splitting quaternion algebras defined over a finite field extension.

We study systems of quadratic forms over fields and their isotropy over 2 -extensions. We apply this to obtain particular splitting fields for quaternion algebras defined over a finite field extension. As a consequence we obtain that every central simple algebra of degree 1 6 is split by a 2 -extension of degree at most 2 1 6 . [ABSTRACT FROM AUTHOR]