Submission: 2013, Nov 6
We show that a non-hyperbolic quadratic pair on a central simple algebra Brauer equivalent to a quaternion algebra stays non-hyperbolic over some splitting field of the quaternion algebra. This extends a result previously only known for fields of characteristic different from two. Our presentation is free from restrictions on the characteristic of the base field.
2010 Mathematics Subject Classification: 11E39, 11E81, 12F05, 12F10
Keywords and Phrases: Central simple algebras, involutions, quadratic pairs, hermitian forms, characteristic two, quaternion algebras, quadratic forms
Full text: dvi.gz 46 k, dvi 111 k, ps.gz 725 k, pdf.gz 206 k, pdf 227 k.