Pathologies of the Brauer-Manin obstruction

Abstract

We construct a conic bundle over an elliptic curve over a real quadratic field that is a counterexample to the Hasse principle not explained by the étale Brauer-Manin obstruction. We also give simple examples of threefolds with the same property that are families of 2-dimensional quadrics, and discuss some other examples and general properties of the Brauer-Manin obstruction.

22 pages, to appear in Mathematische Zeitschrift

References in corpus (2)

• Surjectivity of mod 2^n representations of elliptic curves
• Elliptic curves with 3-adic Galois representation surjective mod 3 but not mod 9

Cited by in corpus (2)

• Weak approximation for homogeneous spaces: reduction to the case with finite stabilizer
• Insufficiency of the étale Brauer-Manin obstruction: towards a simply connected example