Remark 3

Tag 0CO8, permanent. Cite it as [Bourbaki, Tag 0CO8].

Commutative Algebra, chapter VIII, § 4. Séries de Hilbert-Samuel

Let $M(p)$ be the module deduced from M by shifting the grading by $p$ (A, II, p. 165, example 3). Since we have $M(p)_n = M_{p+n}$ , we have $P_{M(p)} = T^{-p}P_M$ , $Q_{M(p)} = T^{-p}Q_M$ and $c_{M(p)} = c_M$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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