J.-L. Colliot-Thélène, M. Ojanguren, R. Parimala: Quadratic forms over fraction fields of two-dimensional henselian rings and Brauer groups of related schemes


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

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