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.

Keywords:

• Primary: 11R23
• Secondary: 11G40, 19B28
• Iwasawa theory
• complex multiplication
• elliptic cures
• K-theory
• L-functions