Pathologies of the Brauer-Manin obstruction

2013/10/18 by Jean-Louis Colliot-Thélène, Colliot-Thélène, Jean-Louis, Ambrus Pál +3
Mathematics · #14F22 #14G05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1310.5055

openalex publication_date 2013/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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