  In this paper we show how one can combine the p-adic Rankin-Selberg product
construction of Hida with freeness results of Hecke modules of Wiles to
establish interesting congruences between special values of L-functions. These
congruences is a part of some deep conjectural congruences that follow from the
work of Kato on the non-commutative Iwasawa theory of the false Tate curve
extension.
