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

Abstract: We develop an explicit descent theory in the context of Whitehead
groups of non-commutative Iwasawa algebras. We apply this theory to describe
the precise connection between main conjectures of non-commutative Iwasawa
theory (in the spirit of Coates, Fukaya, Kato, Sujatha and Venjakob) and the
equivariant Tamagawa number conjecture. The latter result is a converse to
a theorem of Fukaya and Kato and also provides an important means of both
deriving explicit consequences of the main conjecture and proving special cases
of the equivariant Tamagawa number conjecture.
1991 Mathematics Subject Classification: Primary 11G40; Secondary 11R65
19A31 19B28
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