On Grothendieck–Serre conjecture in mixed characteristic

It will be sketched a positive solution of the conjecture for the case of the special linear group corresponding to an Azumaya algebra over an unramified local regular ring $R$ of mixed characteristic.
Particularly, it will be proved that for any units $a$, $b$, $c$ in $R$ the equation $X^2 - aY^2 - bZ^2 +abT^2=c$ has a solution over the fraction field of $R$ if and only if it has a solution over $R$.