Akashi series, characteristic elements and congruence of Galois representations

Abstract

In this paper, we compare the Akashi series of the Pontryagin dual of the Selmer groups of two Galois representations over a strongly admissible p-adic Lie extension. Namely, we show that whenever the two Galois representations in question are congruent to each other, the Akashi series of one is a unit if and only if the Akashi series of the other is also a unit. We will also obtain similar results for the Euler characteristics of the Selmer groups and the characteristic elements attached to the Selmer groups.

19 pages. Final version

References in corpus (2)

• A remark on the ${\mathfrak{M}}_H(G)$-conjecture and Akashi series
• Comparing the Selmer group of a $p$-adic representation and the Selmer group of the Tate dual of the representation

Cited by in corpus (1)

• ${\mathfrak{M}}_H(G)$-property and congruence of Galois representations