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

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

2007-10-25

arxiv.org/abs/0710.4952v1

JIMJ (2010)

Mathematics

Number Theory

43 pages

Scientific paper

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

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