I'm reading the classical paper of Arakelov "Intersection Theory of Divisors on an Arithmetic Surface". At the very beginning he uses the notion of model of a curve.
In specific we have a number field $K$ with ring of integers $R$, $X$ is a smooth complete algebraic curve over $K$. Here Arakelov writes: "Let $V$ be any smooth and complete model of $X$ over $R$."
What does it mean? I didn't find the definition nor googling it, neither looking on the books "Algebraic Geometry" of Hartshorne and "Introduction to Intersection Theory in Algebraic Geometry" of Fulton.