Akashi series, characteristic elements and congruence of Galois representations

摘要

In this paper, we compare the Akashi series of the Pontryagin dual of theSelmer groups of two Galois representations over a strongly admissible p-adicLie extension. Namely, we show that whenever the two Galois representations inquestion are congruent to each other, the Akashi series of one is a unit if andonly if the Akashi series of the other is also a unit. We will also obtainsimilar results for the Euler characteristics of the Selmer groups and thecharacteristic elements attached to the Selmer groups.