The Growth of CM Periods over False Tate Extensions

Abstract

We prove weak forms of Kato's K1-congruences for elliptic curves with complex multiplication, subject to two technical hypotheses. We next use MAGMA to calculate the µ-invariant measuring the discrepancy between the "motivic" and "automorphic" p-adic L-functions. Via the two-variable main conjecture, one can then estimate growth in this µ-invariant using arithmetic of the ℤ2 p -extension.