Definition 10.59.6. Let $R$ be a Noetherian local ring. Let $M$ be a finite $R$-module. The *Hilbert polynomial* of $M$ over $R$ is the element $P(t) \in \mathbf{Q}[t]$ such that $P(n) = \varphi _ M(n)$ for $n \gg 0$.

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