Numerical Evidence Toward a 2-adic Equivariant “Main Conjecture”

Abstract

We test a conjectural nonabelian refinement of the classical 2-adic Main Conjecture of Iwasawa theory. In the first part, we show how, in the special case that we study, the validity of this refinement is equivalent to a congruence condition on the coefficients of some power series. Then, in the second part, we explain how to compute the first coefficients of this power series and thus numerically check the conjecture in that setting.

2000 AMS Subject Classification:

• 11Y40
• 11R23
• 11R70

Keywords:

• algebraic K-theory
• Galois modules
• Iwasawa theory
• p-adic L-functions

ACKNOWLEDGMENTS

The first-named author was supported by projet AlgoL (ANR-07-BLAN-0248). The second-named author gratefully acknowledges financial support from the NSERC.