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We prove a `Weierstrass Preparation Theorem' and develop an explicit descentformalism in the context of Whitehead groups of non-commutative Iwasawaalgebras. We use these results to describe the precise connection between themain conjecture of non-commutative Iwasawa theory (in the sense of Coates,Fukaya, Kato, Sujatha and Venjakob) and the equivariant Tamagawa numberconjecture. The latter result is both a converse to a theorem of Fukaya andKato and also provides an important means of deriving explicit consequences ofthe main conjecture.

On descent theory and main conjectures in non-commutative Iwasawa theory