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

By David Burns, O. Venjakob. Journal of the Institute of Mathematics of Jussieu, 2007

52 citations recorded by the source corpus.

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 both a converse to a theorem of Fukaya and Kato and also provides an important means of deriving explicit consequences of the main conjecture and proving special cases of the equivariant Tamagawa number conjecture.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/17bfd896a38067e80165a6ea6b5aa8b3b7e692e2