The notion of the truncated Euler characteristic for Iwasawa modules is an extension of the notion of the usual Euler characteristic to the case when the homology groups are not finite. This article explores congruence relations between the truncated Euler characteristics for dual Selmer groups of elliptic curves with isomorphic residual representations, over admissible $p$-adic Lie extensions. Our results extend earlier congruence results from the case of elliptic curves with rank zero to the case of higher rank elliptic curves.

中文翻译：

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正秩设置中的欧拉特征及其同余

Iwasawa 模的截断 Euler 特征的概念是通常 Euler 特征的概念在同调群不是有限的情况下的扩展。本文探讨了具有同构残差表示的椭圆曲线的双 Selmer 群的截断 Euler 特征之间的同余关系，在可接受的 $p$-adic Lie 扩展上。我们的结果将早期的同余结果从零阶椭圆曲线的情况扩展到更高阶椭圆曲线的情况。