Submission: 2000, Jun 15
Let A be an excellent henselian two-dimensional local domain, K its field of fractions and k its residue field. We study Azumaya algebras and quadratic forms over K when k is separably closed or real closed. Here are three typical results: a) Assume that k is algebraically closed of characteristic zero. Then any division algebra over K is cyclic. b) Under the same assumption on k, any quadratic form over K of rank at least 5 is isotropic. In rank 3 and 4, a local-global principle holds. c) Assume that k is real closed. Then the u-invariant of K is at most 4.
1991 Mathematics Subject Classification: 11E08, 14F22, 11E12, 14G27
Keywords and Phrases: Brauer group, quadratic form, henselian ring
Full text: dvi.gz 41 k, dvi 98 k, ps.gz 213 k, pdf.gz 239 k, pdf 286 k.