Affiliation:
1. Department of Computer Science, Math and Environmental Science The American University of Paris Paris France
Abstract
AbstractLet k be any field. Let be a degree hypersurface. Under some conditions, we prove that if for some extension with and , then for some extension with , , and . Moreover, if a K‐solution is known explicitly, then we can compute explicitly as well. As an application, we improve upon a result by Coray on smooth cubic surfaces by showing that if for some extension with , then for some with .
Reference6 articles.
1. Algebraic points on cubic hypersurfaces
2. J.‐L.Colliot‐ThélèneandJ.‐J.Sansuc La descente sur les variétés rationnelles Journées de Géométrie Algébrique d'Angers Juillet 1979/Algebraic Geometry Angers 1979 Sijthoff & Noordhoff Alphen aan den Rijn 1980 1979 pp.223–237.
3. The Algebraic and Geometric Theory of Quadratic Forms
4. Closed Points on Cubic Hypersurfaces
5. Persistence of the Brauer–Manin obstruction on cubic surfaces