On Grothendieck--Serre conjecture in mixed characteristic for SL_1(D)
K-Theory and Homology
2022-02-14 v1
Abstract
Let R be an unramified regular local ring of mixed characteristic, D an Azumaya R-algebra, K the fraction field of R, Nrd the reduced norm homomorphism for the Azumaya R-algebra D. Let a be a unit in R. It is proved the following: suppose the equation Nrd=a has a solution over K, then it has a solution over R. Similar results are proved for regular local rings, which are geometrically regular over a discrete valuation ring of mixed characteristic. These results extend result proven by A.Sulin and the author in the middle of 90's.
Keywords
Cite
@article{arxiv.2202.05493,
title = {On Grothendieck--Serre conjecture in mixed characteristic for SL_1(D)},
author = {Ivan Panin},
journal= {arXiv preprint arXiv:2202.05493},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2202.00896