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The notion of the truncated Euler characteristic for Iwasawa modules is anextension of the notion of the usual Euler characteristic to the case when thehomology groups are not finite. This article explores congruence relationsbetween the truncated Euler characteristics for dual Selmer groups of ellipticcurves with isomorphic residual representations, over admissible $p$-adic Lieextensions. Our results extend earlier congruence results from the case ofelliptic curves with rank zero to the case of higher rank elliptic curves.

Euler Characteristics and their Congruences in the Positive Rank Setting