Lemma 48.27.4. Let $k$, $X$, and $\omega _ X^\bullet $ be as in Lemma 48.27.1. Let $t : H^0(X, \omega _ X^\bullet ) \to k$ be as in Remark 48.27.2. Let $E \in D(\mathcal{O}_ X)$ be perfect. Then the pairings

are perfect for all $i$. Here $\cup $ denotes the cupproduct of Cohomology, Section 20.31 and $\epsilon : E^\vee \otimes _{\mathcal{O}_ X}^\mathbf {L} E \to \mathcal{O}_ X$ is as in Cohomology, Example 20.50.7.

## Comments (0)

There are also: