Self-duality of the Koszul complex
= Self-duality of the Koszul complex
{title2=$\operatorname{Hom}_R(K_i,R)\cong K_{r-i}$}
The perfect exterior pairing in complementary degrees identifies the dual of a <Koszul complex> with its degree reversal, with suitable differential signs. For a <regular sequence>, its <Koszul resolution> consequently gives $\operatorname{Ext}_R^i(R/(f),R)=0$ except in degree $r$, where it is $R/(f)$.