On descent theory and main conjectures in non-commutative Iwasawa theory
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 equiv...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2011
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| In: |
Journal of the Institute of Mathematics of Jussieu
Year: 2010, Volume: 10, Issue: 1, Pages: 59-118 |
| ISSN: | 1475-3030 |
| DOI: | 10.1017/S147474800900022X |
| Online Access: | Resolving-System, Volltext: http://dx.doi.org/10.1017/S147474800900022X Verlag, Volltext: https://www.cambridge.org/core/journals/journal-of-the-institute-of-mathematics-of-jussieu/article/on-descent-theory-and-main-conjectures-in-noncommutative-iwasawa-theory/19F4512AD8DE790FC94CF88AD004BD45 
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| Author Notes: | David Burns and Otmar Venjakob |
| Summary: | 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. |
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| Item Description: | Published online: 26 April 2010 Gesehen am 14.02.2019 |
| Physical Description: | Online Resource |
| ISSN: | 1475-3030 |
| DOI: | 10.1017/S147474800900022X |