A positive proportion of Hasse principle failures in a family of Châtelet surfaces

Nick Rome

doi:10.1142/S1793042119500684

A positive proportion of Hasse principle failures in a family of Châtelet surfaces

Nick Rome^*

^*Corresponding author for this work

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Abstract

We investigate a family of Châtelet surfaces over Q and develop an asymptotic formula for the frequency of Hasse principle failures. We show that a positive proportion (roughly 23.7%) of such surfaces fails the Hasse principle, by building on previous work of De La Bretèche and Browning.

Original language	English
Pages (from-to)	1237-1249
Number of pages	13
Journal	International Journal of Number Theory
Volume	15
Issue number	6
Early online date	13 Feb 2019
DOIs	https://doi.org/10.1142/S1793042119500684
Publication status	Published - 1 Jul 2019

Keywords

Brauer-Manin obstruction
Châtelet surfaces
Hasse principle

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10.1142/S1793042119500684

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This is the accepted author manuscript (AAM). The final published version (version of record) is available online via World Scientific at https://doi.org/10.1142/S1793042119500684 . Please refer to any applicable terms of use of the publisher.
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https://arxiv.org/abs/1803.07017

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abstract = "We investigate a family of Ch{\^a}telet surfaces over Q and develop an asymptotic formula for the frequency of Hasse principle failures. We show that a positive proportion (roughly 23.7\%) of such surfaces fails the Hasse principle, by building on previous work of De La Bret{\`e}che and Browning.",

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N2 - We investigate a family of Châtelet surfaces over Q and develop an asymptotic formula for the frequency of Hasse principle failures. We show that a positive proportion (roughly 23.7%) of such surfaces fails the Hasse principle, by building on previous work of De La Bretèche and Browning.

AB - We investigate a family of Châtelet surfaces over Q and develop an asymptotic formula for the frequency of Hasse principle failures. We show that a positive proportion (roughly 23.7%) of such surfaces fails the Hasse principle, by building on previous work of De La Bretèche and Browning.

KW - Brauer-Manin obstruction

KW - Châtelet surfaces

KW - Hasse principle

UR - https://www.scopus.com/pages/publications/85061693896

U2 - 10.1142/S1793042119500684

DO - 10.1142/S1793042119500684

M3 - Article (Academic Journal)

AN - SCOPUS:85061693896

SN - 1793-0421

VL - 15

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EP - 1249

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 6

ER -

A positive proportion of Hasse principle failures in a family of Châtelet surfaces

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Keywords

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