English

Beyond the Manin obstruction

alg-geom 2007-05-23 v1 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.alg-geom/9711006,
  title  = {Beyond the Manin obstruction},
  author = {Alexei Skorobogatov},
  journal= {arXiv preprint arXiv:alg-geom/9711006},
  year   = {2007}
}

Comments

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