How does the line bundles look like on a proper model (or Néron model) of an abelian variety?

Who knows references about this?

In particular, let us work over a trait $S=\mathrm{Spec} R$, where $R$ is a DVR, with generic point $\eta=\mathrm{Spec}K$ and special point $s=\mathrm{Spec}k$. Given an semistable abelian variety $A_K$ over $K$, we have the Néron model $A$ over $S$, and other proper models over $S$, take one proper model say $E$. Given a line bundle on $A$ or $E$, they restricts to a line bundle on $A_K$. Now when a line bundle on $A_K$ come from a line bundle on $A$ or $E$.