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

       Autors: D. Burns, O. Venjakob
       Titel:  On descent theory and main conjectures in non-commutative Iwasawa theory
       Jahr: 2005
       Seiten: 38
       In: "Journal of the Institute of Mathematics of Jussieu, volume 10, issue 01, pp. 59-118. © Cambridge University Press 2010, doi:10.1017/S147474800900022X
     

      
      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 In

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