Beyond the Manin obstruction

Details Beyond the Manin obstruction Beyond the Manin obstruction

1997-11-05

arxiv.org/abs/alg-geom/9711006v1

Mathematics

Algebraic Geometry

Plain TeX, 15 pages, an appendix by S. Siksek

Scientific paper

We construct a (smooth, projective) surface over the field of rational numbers, which is a counterexample to the Hasse principle not accounted for by the Manin obstruction. The construction relies on the classical 4-descent on elliptic curves. By combining the Manin obstruction with descent we define a refinement of the Manin obstruction which for surfaces of the type considered suffices to explain the absence of a rational point.

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