A heuristic for boundedness of ranks of elliptic curves
A heuristic for boundedness of ranks of elliptic curves
复制标题
DOI：
10.4171/jems/893
复制
发表时间：
2016-02
影响因子：
2.6
通讯作者：
Jennifer Park;B. Poonen;J. Voight;M. Wood
中科院分区：
文献类型：
--
作者：
Jennifer Park;B. Poonen;J. Voight;M. Wood
我们提出了一种启发式方法，表明有理数上的椭圆曲线的等级是有界的。事实上，它表明只有有限多个秩大于 21 的椭圆曲线。我们的启发式基于同时对椭圆曲线的秩和 Shafarevich-Tate 群进行建模，并依赖于对指定秩的交替整数矩阵进行计数的定理。我们还讨论了其他全球领域的椭圆曲线的类似物。
We present a heuristic that suggests that ranks of elliptic curves over the rationals are bounded. In fact, it suggests that there are only finitely many elliptic curves of rank greater than 21. Our heuristic is based on modeling the ranks and Shafarevich-Tate groups of elliptic curves simultaneously, and relies on a theorem counting alternating integer matrices of specified rank. We also discuss analogues for elliptic curves over other global fields.