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Let R be an unramified regular local ring of mixed characteristic, D anAzumaya R-algebra, K the fraction field of R, Nrd the reduced norm homomorphismfor 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 overR.  Similar results are proved for regular local rings, which are geometricallyregular over a discrete valuation ring of mixed characteristic. These resultsextend result proven by A.Sulin and the author in the middle of 90's.

On Grothendieck--Serre conjecture in mixed characteristic for SL_1(D)