论文标题
班级组的渐近行为和椭圆曲线的环流岩川理论
Asymptotic behavior of class groups and cyclotomic Iwasawa theory of elliptic curves
论文作者
论文摘要
在本文中，我们研究了理想班级的某些商与奇异岛模块的某些商之间的关系，$ x_ \ infty $的pontrjagin dual dual the Elliptic Curve $ e $的精细Selmer dual dual dual dual dual $ \ mathbb {q} $。我们考虑$ \ mathbb {q} $的GALOIS扩展字段$ k^e_n $由$ e $的所有$ p^n $ torsion点生成，并引入了$ k^e_n $ $ $ $ $ $ $ $ p^n] $ p $ -sylow子组的$ p $ - sylow子组的商$ a^e_n $的$ a^e_n $。我们使用iwasawa模块$ x_ \ infty $描述了$ a^e_n $的渐近行为。特别是，在某些条件下，我们通过使用iwasawa的不变性$ x_ \ infty $获得了iwasawa的iwasawa的班级班级公式。
In this article, we study a relation between certain quotients of ideal class groups and the cyclotomic Iwasawa module $X_\infty$ of the Pontrjagin dual of the fine Selmer group of an elliptic curve $E$ defined over $\mathbb{Q}$. We consider the Galois extension field $K^E_n$ of $\mathbb{Q}$ generated by coordinates of all $p^n$-torsion points of $E$, and introduce a quotient $A^E_n$ of the $p$-sylow subgroup of the ideal class group of $K^E_n$ cut out by the modulo $p^n$ Galois representation $E[p^n]$. We describe the asymptotic behavior of $A^E_n$ by using the Iwasawa module $X_\infty$. In particular, under certain conditions, we obtain an asymptotic formula as Iwasawa's class number formula on the order of $A^E_n$ by using Iwasawa's invariants of $X_\infty$.
