FROM SEPARABLE POLYNOMIALS TO NONEXISTENCE OF RATIONAL POINTS ON CERTAIN HYPERELLIPTIC CURVES

被引：1
作者：
Quan, Nguyen Ngoc Dong [1 ]
机构：
[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
来源：
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2014年 / 96卷 / 03期
关键词：
Azumaya algebras; Brauer groups; Brauer-Manin obstruction; Hasse principle; hyperelliptic curves; HASSE PRINCIPLE;
D O I：
10.1017/S1446788714000044
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a separability criterion for the polynomials of the form ax(2n+2) + (bx(2m) + c)(dx(2k) + e). Using this separability criterion, we prove a sufficient condition using the Brauer-Manin obstruction under which curves of the form z(2) = ax(2n+2) + (bx(2m) + c)(dx(2k) + e) have no rational points. As an illustration, using the sufficient condition, we study the arithmetic of hyperelliptic curves of the above form and show that there are infinitely many curves of the above form that are counterexamples to the Hasse principle explained by the Brauer-Manin obstruction.
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页码：354 / 385
页数：32
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