\title{Nilpotence and generation in the stable module category}
\author{David J. Benson}
\address{Institute of Mathematics, Fraser Noble Building, Univeristy
  of Aberdeen, Aberdeen AB24 3UE, United Kingdom}
\author{Jon F. Carlson}
\address{Department of Mathematics, University of Georgia, Athens GA
  30602, USA}
\thanks{The second author was partially supported by NSA grant 
H98230-15-1-0007 and Simons Foundation grant 315728}
\begin{document}

\begin{abstract}
Nilpotence has been studied in stable homotopy theory and algebraic
geometry. We study the corresponding notion in modular
representation theory of finite groups, and apply the discussion to
the study of ghosts, and generation of the stable module category.
In particular, we show that for a finitely generated $kG$-module $M$,
the tensor $M$-generation number and the tensor $M$-ghost number are
both equal to the degree of tensor nilpotence of a certain map
associated
with $M$.
\end{abstract}