The Brauer–Manin obstruction for integral points on curves
The Brauer–Manin obstruction for integral points on curves
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DOI：
10.1017/s0305004110000381
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发表时间：
2010-06
影响因子：
0.8
通讯作者：
David Harari;J. Voloch
中科院分区：
文献类型：
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作者：
David Harari;J. Voloch
本文讨论了Brauer-Manin障碍是否是仿射双曲曲线上整点的Hasse原理的唯一障碍。在合理的曲线的情况下，我们猜想一个积极的答案，我们证明，这个猜想可以给出几个等价的配方，我们将它与一个老猜想的Skolem。最后，我们表明，椭圆曲线减去一个点的强版本的问题（描述的一组积分点的局部条件）有一个否定的答案。
Abstract We discuss the question of whether the Brauer–Manin obstruction is the only obstruction to the Hasse principle for integral points on affine hyperbolic curves. In the case of rational curves we conjecture a positive answer, we prove that this conjecture can be given several equivalent formulations and we relate it to an old conjecture of Skolem. Finally, we show that for elliptic curves minus one point a strong version of the question (describing the set of integral points by local conditions) has a negative answer.