On factorizations of certain Kummer characters associated to once-punctured elliptic curves with complex multiplication

Abstract

In this paper, we study certain Kummer characters, which we call the elliptic Soulé characters, arising from Galois actions on the pro-$p$ fundamental groups of once-punctured elliptic curves with complex multiplication. In particular, we prove that elliptic Soulé characters having values in Tate twists can be written in terms of the Soulé characters and generalized Bernoulli numbers. We apply this result to give a criterion for surjectivity of the elliptic Soulé characters and an analogue of the Coleman-Ihara formula.

20 pages