Karim Johannes Becher, Andrew Dolphin: Non-hyperbolic splitting of quadratic pairs


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

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