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Weak approximation for surfaces defined by two quadratic forms. (English) Zbl 0770.14019

The aim of this paper is to prove a conjecture due to J.-L. Colliot- Thélène, J.-J. Sansuc and P. Swinnerton-Dyer about weak approximation on del Pezzo surfaces of degree 4. The main result shows that, if such a surface defined over a number field has at least one point over that field, then the “Brauer obstruction” is the only obstruction to weak approximation.

MSC:

14J20 Arithmetic ground fields for surfaces or higher-dimensional varieties
14M10 Complete intersections
14J25 Special surfaces
14G25 Global ground fields in algebraic geometry
14G20 Local ground fields in algebraic geometry
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