  The Grothendieck--Serre conjecture predicts that every generically trivial
torsor under a reductive group scheme $G$ over a regular local ring $R$ is
trivial. The mixed characteristic case of the conjecture is widely open. We
consider the following setup. Let $A$ be a mixed characteristic DVR, $G$ a
reductive group scheme over $A$, $X$ an irreducible smooth projective
$A$-scheme, $\mathcal G$ a principal $G$-bundle over $X$. Suppose $\mathcal G$
is generically trivial. We prove that in this case $\mathcal G$ is Zariski
locally trivial. This result confirms the conjecture.
