Growth of $unicode[STIX]{x0428}$ in towers for isogenous curves
Growth of $unicode[STIX]{x0428}$ in towers for isogenous curves
复制标题
$unicode[STIX]{x0428}$ 在同源曲线塔中的增长
作者：
T. Dokchitser;V. Dokchitser
我们在数域的塔上研究了同源交换变种的$Unicode[stix]{x0428}$和$p^{infty}$-Selmer群的增长性，重点讨论了椭圆曲线.增长类型通常是指数型的，就像岩泽椭圆曲线理论中的“正${itu}$-不变‘设置一样。我们考虑的塔是$p$-adic和$L$-adic李扩张，它是$L的
等式p$，特别是割圆和其他$mathbb{Z}_{L}$-扩张。
We study the growth of $unicode[STIX]{x0428}$ and $p^{infty }$-Selmer groups for isogenous abelian varieties in towers of number fields, with an emphasis on elliptic curves. The growth types are usually exponential, as in the ‘positive ${itmu}$-invariant’ setting in the Iwasawa theory of elliptic curves. The towers we consider are $p$-adic and $l$-adic Lie extensions for $l
eq p$, in particular cyclotomic and other $mathbb{Z}_{l}$-extensions.