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

被引：1

作者：

Rome, Nick ^{[1
]}

机构：

[1] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2019年 / 15卷 / 06期

基金：

英国工程与自然科学研究理事会;

关键词：

Hasse principle; Chatelet surfaces; Brauer-Manin obstruction;

D O I：

10.1142/S1793042119500684

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate a family of Chatelet 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 Breteche and Browning.

引用

页码：1237 / 1249

页数：13

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