科研之友
微信
新浪微博
Facebook
分享链接
摘要
In 2000, Colliot-Thelene and Poonen showed how to construct algebraic families of genus-one curves violating the Hasse principle. Poonen explicitly constructed such a family of cubic curves using the general method developed by Colliot-Thelene and himself. The main result in this paper generalizes the result of Colliot-Thelene and Poonen to arbitrarily high genus hyperelliptic curves. More precisely, for n > 5 and n 6 not equivalent to 0 (mod 4), we show that there is an explicit algebraic family of hyperelliptic curves of genus n that are counterexamples to the Hasse principle explained by the Brauer-Manin obstruction.
- 出版日期2015-3
