Euler Characteristics and their Congruences in the Positive Rank Setting

Abstract

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.

19 pages, submitted, minor changes for the benefit of exposition

References in corpus (1)

• Fine Selmer groups of congruent Galois representations

Cited by in corpus (2)

• Euler Characteristics and their Congruences for Multi-signed Selmer Groups
• Arithmetic statistics and diophantine stability for elliptic curves