The third homology of SL₂ of local rings

2013/09/19 by Kevin Hutchinson-Lhuissier, Hutchinson, Kevin · 2 citations
Mathematics · #19G99 #20G10 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1309.5010

openalex publication_date 2013/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the third homology of SL₂ of local rings over Z[1/2] in terms of a refined Bloch group. We use this to derive a localization sequence for the third homology of SL₂ of certain discrete valuation rings, and to make explicit computations for p-adic integers and other local rings.

Cited by

• Schur multiplier of SL₂ over finite commutative rings
• Low-dimensional Homology of SL₂(k[t,1/t])

Related

• Bloch Groups of Rings
• The third homology of SL₂ of fields with discrete valuation
• A refined Bloch group and the third homology of SL₂ of a field
• A refined Bloch-Wigner exact sequence in characteristic 2
• The low dimensional homology of projective linear group of rank two