becher@maths.ucd.i, mohammad.mahmoudi@ucd.ie

Submission: 2005, Jun 27, revised 2008, Apr 23

In quadratic form theory over fields, a much studied field invariant is the u-invariant, defined as the supremum over the dimensions of anisotropic quadratic forms over the field. We investigate the corresponding notions of u-invariant for hermitian and for skew-hermitian forms over a division algebra with involution, with a special focus on skew-hermitian forms over a quaternion algebra. Under certain conditions on the center of the quaternion algebra, we obtain sharp bounds for this invariant.

2000 Mathematics Subject Classification: 11E04, 11E39, 11E81

Keywords and Phrases: hermitian form, isotropy, dimension, algebra with involution, $u$-invariant

Full text: dvi.gz 29 k, dvi 67 k, ps.gz 615 k, pdf.gz 163 k, pdf 184 k.

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