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arXiv · 1803.07017

A Positive Proportion of Hasse Principle Failures in a Family of Châtelet Surfaces

Nick Rome
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Abstract

We investigate the family of surfaces defined by the affine equation $$Y^2 + Z^2 = (aT^2 + b)(cT^2 +d)$$ where $\vert ad-bc \vert=1$ and develop an asymptotic formula for the frequency of Hasse principle failures. We show that a positive proportion (roughly 23.7%) of such surfaces fail the Hasse principle, by building on previous work of la Bretèche and Browning.

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Nick Rome. 2019-02-22. A Positive Proportion of Hasse Principle Failures in a Family of Châtelet Surfaces. https://doi.org/10.1142/s1793042119500684

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