Acta Mathematica Vietnamica
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A Remark on Vanishing of Chain Complexes
Yuji Yoshinopp. 173-177
Abstract
For chain complexes $W \in D^{\pm} _{fg} (R)$ and $X \in D(R)$ in the derived category over a commutative noetherian ring $R$, we prove that $\mathrm{RHom} _R (W, X) = 0$ if and only if $W {\, {}^{\mathrm L}\otimes}_R X =0$.