Third homology of SL₂ over Number fields: The norm-Euclidean quadratic imaginary case

2022/12/15 by Coronado, Rodrigo Cuitun
#19F99 #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2212.07819

Abstract

In the article The third homology of SL₂(ℚ), Hutchinson determined the structure of H₃(SL₂(ℚ),ℤ[(1)/(2)]) by expressing it in terms of K₃^ind(ℚ)≅ ℤ/24 and the scissor congruence group of the residue field \mathbbF_p with p a prime number. In this paper, we develop further the properties of the refined scissors congruence group in order to extend this result to the case of imaginary quadratic number fields whose ring of integers is a Euclidean domain with respect to the norm.

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