Thoughts on the reduced Whitehead group of the Iwasawa algebra
Irene Lau

TL;DR
This paper discusses the properties of the reduced Whitehead group of Iwasawa algebras associated with certain Galois extensions, reducing the problem to cases with pro-l Galois groups and finite unramified extensions.
Contribution
It reduces the conjecture on the triviality of SK_1(QG) for Iwasawa algebras to simpler cases involving pro-l Galois groups and unramified extensions.
Findings
Reduces the conjecture to pro-l Galois groups case
Simplifies the problem to unramified coefficient extensions
Provides a framework for further investigation of SK_1(QG)
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_\infty and k/Q are finite. We reduce the conjectured triviality of the reduced Whitehead group SK_1(QG) of the algebra QG=Quot(\Lambda G) with the Iwasawa algebra \Lambda G = Z_l[[G]] to the case of pro-l Galois groups G and finite unramified coefficient extensions.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
