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The Stacks project

Remark 75.15.2. The proof of Lemma 75.15.1 shows that

R|_ W = P \oplus P^{\oplus n_1}[1] \oplus \ldots \oplus P^{\oplus n_ m}[m]

for some m \geq 0 and n_ j \geq 0. Thus the highest degree cohomology sheaf of R|_ W equals that of P. By repeating the construction for the map P^{\oplus n_1}[1] \oplus \ldots \oplus P^{\oplus n_ m}[m] \to R|_ W, taking cones, and using induction we can achieve equality of cohomology sheaves of R|_ W and P above any given degree.


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