K₁-congruences for three-dimensional Lie groups
Delbourgo, D., & Chao, Q. (2019). K₁-congruences for three-dimensional Lie groups. Annales Mathématiques Du Québec, 43(1), 161–211. https://doi.org/10.1007/s40316-018-0100-y
Permanent Research Commons link: https://hdl.handle.net/10289/12526
We completely describe K₁ (Zₚ [[G∞]]) and its localisations by using an infinite family of p-adic congruences, where G∞ is any solvable p-adic Lie group of dimension 3. This builds on earlier work of Kato when dim(G∞)=2 , and of the first named author and Lloyd Peters when G∞≅Z×p⋉Z𝒹ₚ with a scalar action of Z×ₚ . The method exploits the classification of 3-dimensional p-adic Lie groups due to González-Sánchez and Klopsch, as well as the fundamental ideas of Kakde, Burns, etc. in non-commutative Iwasawa theory.
© Fondation Carl-Herz and Springer International Publishing AG, part of Springer Nature 2018.This is the author's accepted version. The final publication is available at Springer via dx.doi.org/10.1007/s40316-018-0100-y