Localization–completion strikes again: Relative K1 is nilpotent by abelian

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Structure of Chevalley groups over rings via universal localization (2013, background): “tent provided that Gis simply connected. A nilpotent ﬁltration was obtained by A.Bak in [5] for G= SLn and by R.Hazrat and N.Vavilov in [16] for all Chevalley 3 groups. A relative version appeared in [7] by the three authors. We generalize all results on the nilpotent structure of KG 1 mentioned abo”
Affine representability results in 1–homotopy theory, II : Principal bundles and homogeneous spaces (2015, unknown): “In this section, we include one more sample application of our results: we give a uniform proof of some nilpotence results for non-stable K1 –functors discussed in the previous section; such nilpotence results have been studied for instance by Bak [11] and Bak–Hazrat–Vavilov [12].”