  Let S be the spectrum of a discrete valuation ring with function field K. Let
X be a scheme over S. We will say that X is semi-factorial over S if each
invertible sheaf on the generic fiber X_K can be extended to an invertible
sheaf on X. Here we show that any proper geometrically normal scheme over K
admits a model over S which is proper, flat, normal and semi-factorial. We also
construct some semi-factorial compactifications of regular S-schemes, such as
N\'eron models of abelian varieties. Moreover, the semi-factoriality property
for a scheme X/S corresponds to the N\'eron property of its Picard functor. In
particular, one can recover the N\'eron model of the Picard variety of X_K from
the Picard functor of X/S, as in the case of curves. This provides some
information about relative algebraic equivalence on the S-scheme X.
