Néron model

A Néron model is a mathematical tool used in number theory and algebraic geometry to extend a smooth, well-behaved object called an abelian variety (a type of algebraic structure) from a number field to its ring of integers. Essentially, it provides the best possible "spread-out" version of this object over a larger domain, ensuring that certain functions behave consistently. This construction helps mathematicians understand how varieties behave not only over fields but also at places where they might have singularities or degenerations, offering a way to study their properties in a more comprehensive setting.