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
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