Hasse principle violations in twist families of superelliptic curves

被引:0
作者
Watson, Lori D. [1 ]
机构
[1] Trinity Coll, Dept Math, 300 Summit St, Hartford, CT 06106 USA
基金
美国国家科学基金会;
关键词
Hasse Principle; local-to-global principle; superelliptic curves; twists;
D O I
10.1142/S1793042123500999
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Conditionally on the abc conjecture, we generalize the previous work of Clark and the author to show that a superelliptic curve C : y(n) = f(x) of sufficiently high genus has infinitely many twists violating the Hasse Principle if and only if f(x) has no DOUBLE-STRUCK CAPITAL Q-rational roots. We also show unconditionally that a curve defined by C : ypN = f(x) (for p prime and N > 1) has infinitely many twists violating the Hasse Principle over any number field k such that k contains the pth roots of unity and f(x) has no k-rational roots.
引用
收藏
页码:2051 / 2060
页数:10
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