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arXiv · 1510.03769

On Birch and Swinnerton-Dyer's cubic surfaces

Mckenzie West
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Abstract

In a 1975 paper of Birch and Swinnerton-Dyer, a number of explicit norm form cubic surfaces are shown to fail the Hasse Principle. They make a correspondence between this failure and the Brauer--Manin obstruction, recently discovered by Manin. We generalize their work, making use of modern computer algebra software to show that a larger set of cubic surfaces have a Brauer--Manin obstruction to the Hasse principle, thus verifying the Colliot-Thélène--Sansuc conjecture for infinitely many cubic surfaces.

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Mckenzie West. 2017-03-02. On Birch and Swinnerton-Dyer's cubic surfaces. https://doi.org/10.1007/978-3-319-74998-3_10

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