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Hasse principle for three classes of varieties over global function fields. (English) Zbl 1451.14075

Summary: We give a geometric proof that the Hasse principle holds for the following varieties defined over global function fields: smooth quadric hypersurfaces, smooth cubic hypersurfaces of dimension at least 4 in characteristic at least 7, and smooth complete intersections of two quadrics, which are of dimension at least 3, in odd characteristics.

MSC:

14G12 Hasse principle, weak and strong approximation, Brauer-Manin obstruction
14M22 Rationally connected varieties
14D10 Arithmetic ground fields (finite, local, global) and families or fibrations
14M10 Complete intersections
14G05 Rational points
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