Scheiderer, Claus (1996) Hasse principles and approximation theorems for homogeneous spaces over fields of virtual cohomological dimension one. INVENTIONES MATHEMATICAE, 125 (2). pp. 307-365. ISSN 0020-9910, 1432-1297
Full text not available from this repository.Abstract
Let k be a perfect field with cd k(i) less than or equal to 1. We say that a k-variety X satisfies the Hasse principle if either X(k(xi)) = empty set for some real closure k(xi) of k, or if X(k) not equal empty set. Let G be a connected linear group over k. We prove that every homogeneous space under G, defined over k, satisfies the Hasse principle. This confirms a conjecture of Colliot-Thelelene. In particular, the restriction map H-1(k, G) --> Pi H-1(k(xi), G) is injective, where the product is taken over the real closures of k. We also determine the image of this map and thereby express H-1(k, G) completely in terms of the orderings of k. As applications of these results we prove several approximation theorems for homogeneous spaces (weak approximation, component approximation).
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FORMS |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Jul 2023 10:04 |
| Last Modified: | 05 Jul 2023 10:04 |
| URI: | https://pred.uni-regensburg.de/id/eprint/51674 |
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