\title{Modules of constant Jordan type and a conjecture of Rickard}
\author{David J. Benson}
\address{Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3UE}
\begin{document}
\begin{abstract}
We prove a special case of a conjecture of Rickard on modules of constant
Jordan type over an elementary abelian $p$-group of rank at least $2$.
Namely, we show that if there are no Jordan blocks of length one, then
the total number of Jordan blocks is divisible by $p$. We combine this
with other techniques to rule out a large number of Jordan types.
\end{abstract}