Mohammad Mahmoudi: Hermitian forms and the u-invariant

mohammad.mahmoudi@ucd.ie

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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