\author{D.J.Benson}
\address{Department of Mathematics, University of Aberdeen, Aberdeen AB24 3UE,
UK}


\author{J.P.C.Greenlees}
\address{School of Mathematics and Statistics, Hicks Building, 
Sheffield S3 7RH, UK}


\begin{abstract}
We propose a definition of when a triangulated category should be
considered a complete intersection. We show that for the derived category 
of a complete local Noetherian commutative ring $R$,  
the condition on the derived
category $D(R)$ holds precisely when $R$ is 
a complete intersection in the classical sense. 
\end{abstract}