Scheiderer, Claus (1996) Classification of hermitian forms and semisimple groups over fields of virtual cohomological dimension one. MANUSCRIPTA MATHEMATICA, 89 (3). pp. 373-394. ISSN 0025-2611, 1432-1785
Full text not available from this repository.Abstract
Let k be a perfect field with cd k(i) less than or equal to 1. It has recently been proved by the author that homogeneous spaces under connected linear groups over k satisfy a Hasse principle with respect to the real closures of k. Using this result we classify the semisimple algebraic groups over k and, in particular, characterize the anisotropic ones. Similarly we classify the various types of hermitian forms over skew fields over k and exhibit to what extent weak or strong local-global principles hold. In the case where k is the function field of a smooth projective curve X over R, we also cover the local-global questions vis-a-vis the completions of k at the points of X.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | REAL |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Nov 2023 09:57 |
| Last Modified: | 07 Nov 2023 09:57 |
| URI: | https://pred.uni-regensburg.de/id/eprint/51898 |
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