  We introduce a new method to study mixed characteristic deformation of line
bundles. In particular, for sufficiently large smooth projective families $f :
\mathcal{X} \to \mathcal{S}$ defined over the ring of $N$-integers
$\mathcal{O}_{L}[1/N]$ of a number field $L$, we produce a proper closed
subscheme $\mathcal{E} \subsetneq \mathcal{S}$ outside of which all line
bundles appearing in positive characteristic fibres of $f$ admit characteristic
zero lifts. This in particular applies to elliptic surfaces over $\mathbb{P}^1$
and projective hypersurfaces in $\mathbb{P}^3$ of degree $d \geq 5$. We also
study the locus in $\mathcal{E}$ in more detail in the $h^{0, 2} = 2$ case.
