Lemma 93.8.4. In Example 93.8.1 let $P$ be a smooth $k$-algebra. Then $T\mathcal{D}\! \mathit{ef}_ P = (0)$.
Proof. By Lemma 93.8.3 we have to show $\text{Ext}^1_ P(\mathop{N\! L}\nolimits _{P/k}, P) = (0)$. Since $k \to P$ is smooth $\mathop{N\! L}\nolimits _{P/k}$ is quasi-isomorphic to the complex consisting of a finite projective $P$-module placed in degree $0$. $\square$
Comments (0)