论文标题
Euler特征及其对多签名的Selmer组的一致性
Euler Characteristics and their Congruences for Multi-signed Selmer Groups
论文作者
论文摘要
Iwasawa模块的截断Euler特征的概念是对同居组不是有限的情况的常规欧拉特征的概括。 Let $p$ be an odd prime, $E_1$ and $E_2$ be elliptic curves over a number field $F$ with semistable reduction at all primes $v|p$ such that the $\operatorname{Gal}(\bar{F}/F)$-modules $E_1[p]$ and $E_2[p]$ are irreducible and isomorphic.我们比较了某些不可或缺的多签名Selmer组的Iwasawa不变性，该组为$ e_1 $和$ e_2 $。利用这些结果，研究了与这些Selmer组相关的截短的Euler特征，这是一定的$ \ Mathbb {Z} _p^m $ - $ f $的extensions。我们的结果将椭圆曲线的较早一致关系扩展到$ \ mathbb {q} $上，并以$ p $为单位。
The notion of the truncated Euler characteristic for Iwasawa modules is a generalization of the the usual Euler characteristic to the case when the cohomology groups are not finite. Let $p$ be an odd prime, $E_1$ and $E_2$ be elliptic curves over a number field $F$ with semistable reduction at all primes $v|p$ such that the $\operatorname{Gal}(\bar{F}/F)$-modules $E_1[p]$ and $E_2[p]$ are irreducible and isomorphic. We compare the Iwasawa invariants of certain imprimitive multisigned Selmer groups of $E_1$ and $E_2$. Leveraging these results, congruence relations for the truncated Euler characteristics associated to these Selmer groups over certain $\mathbb{Z}_p^m$-extensions of $F$ are studied. Our results extend earlier congruence relations for elliptic curves over $\mathbb{Q}$ with good ordinary reduction at $p$.
