For questions related to the Néron model (or Néron minimal model, or minimal model). The Néron model for an abelian variety $A_K$ defined over the field of fractions $K$ of a Dedekind domain $R$ is the "push-forward" of $A_K$ from $\text{Spec}(K)$ to $\text{Spec}(R)$.
Suppose that $R$ is a Dedekind domain with field of fractions $K$, and suppose that $A_K$ is a smooth separated scheme over $K$ (such as an abelian variety). Then a Néron model of $A_K$ is defined to be a smooth separated scheme $A_R$ over $R$ with fiber $A_K$ that is universal in the following sense:
If $X$ is a smooth separated scheme over $R$ then any $K$-morphism from $X_K$ to $A_K$ can be extended to a unique $R$-morphism from $X$ to $A_R$ (Néron mapping property).
For more, check out this link.