Thoughts on the reduced Whitehead group of the Iwasawa algebra

2011/01/08 by Irene Lau, Lau, Irene
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1101.1598

openalex publication_date 2011/01/08 · arxiv created 2011/09/24 · arxiv updated 2011/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let l be an odd prime and K/k a Galois extension of totally real number fields with Galois group G such that K/k_∞ and k/Q are finite. We reduce the conjectured triviality of the reduced Whitehead group SK₁(QG) of the algebra QG=Quot(ΛG) with the Iwasawa algebra ΛG = Z_l[[G]] to the case of pro-l Galois groups G and finite unramified coefficient extensions.

Citations

• On the 'main conjecture' of equivariant Iwasawa theory

Related

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• Proof of the Main Conjecture of Noncommutative Iwasawa Theory for Totally Real Number Fields in Certain Cases
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