\title[derived equivalences and Reynolds ideals]{Invariance
of generalised Reynolds ideals\\ under derived equivalences}

\author[Alexander Zimmermann]{Alexander Zimmermann}
\address{Universit\'e de Picardie,\newline  Facult\'e de Math\'ematiques et
LAMFA (UMR 6140 du CNRS),\newline    33 rue St Leu, \newline  F-80039
Amiens Cedex 1, \newline  France}

Accepted in the
MATHEMATICAL PROCEEDINGS OF THE ROYAL IRISH ACADEMY
http://www.ria.ie/publications/journals/procai/index.html

\begin{abstract}
For any algebraically closed field $k$ of
positive characteristic $p$ and any non negative integer
$n$ K\"ulshammer defined ideals $T_nA^\perp$ of the centre of a
symmetric $k$-algebra $A$. We show that for derived equivalent
algebras $A$ and $B$
there is an isomorphism of the centres of $A$
and $B$ mapping $T_nA^\perp$ to $T_nB^\perp$ for all $n$.
Recently H\'ethelyi, Horv\'ath, K\"ulshammer and
Murray showed that this holds for Morita equivalent algebras.
\end{abstract}