Submission: 2005, Mar 9
We study the notion of hermitian $u$-invariant. We give some estimates of the $u$-invariant of a division algebra with involution in terms of the $u$-invariant of some subalgebras stable under the involution. We also find some finiteness results for comparing the $u$-invariant of a division algebra with involution and that of its centre. Some results about the values of this invariant are also given. A description of the Tits index of some algebraic groups of classical type over $Q_p(t)$, $p\neq 2$ is given as an application.
2000 Mathematics Subject Classification: 11E39, 11E81, 11E57
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