Lemma 48.17.3. In Situation 48.16.1 let Y be an object of \textit{FTS}_ S and let f : X = \mathbf{A}^1_ Y \to Y be the projection. Then there is a (noncanonical) isomorphism f^!(-) \cong Lf^*(-) [1] of functors.
Proof. Since X = \mathbf{A}^1_ Y \subset \mathbf{P}^1_ Y and since \mathcal{O}_{\mathbf{P}^1_ Y}(-2)|_ X \cong \mathcal{O}_ X this follows from Lemmas 48.15.1 and 48.13.3. \square
Comments (0)