Euler characteristics and their congruences for multisigned Selmer groups

The notion of the truncated Euler characteristic for Iwasawa modules is a generalization of the the usual Euler characteristic to the case when the Selmer 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 vertical bar p such that the Gal((F) over bar /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 Z(p)(m)-extensions of F are studied. Our results extend earlier congruence relations for elliptic curves over Q with good ordinary reduction at p.