The Stacks project

Example 10.58.9. Suppose that $S = k[X_1, \ldots , X_ d]$. By Example 10.55.2 we may identify $K_0(k) = K'_0(k) = \mathbf{Z}$. Hence any finitely generated graded $k[X_1, \ldots , X_ d]$-module gives rise to a numerical polynomial $n \mapsto \dim _ k(M_ n)$.