Mohammad Mahmoudi: Hermitian forms and the u-invariant

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

Keywords and Phrases:

Full text: dvi.gz 52 k, dvi 141 k, ps.gz 806 k, pdf.gz 223 k, pdf 324 k.

Server Home Page