Euler characteristics and their congruences for multisigned Selmer groups

Ray, Anwesh  ; Sujatha, R.

Canadian journal of mathematics, Tome 75 (2023) no. 1, pp. 298-321

Résumé

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 $v|p$ such that the $\operatorname {Gal}(\overline {F}/F)$-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.

Détail

DOI : 10.4153/S0008414X21000699

Mots-clés : Euler characteristics in Iwasawa theory, congruences, multisigned selmer groups, Iwasawa invariants