\title{Cohomology of Hecke algebras}
\author{Dave Benson}
\author{Karin Erdmann}
\author{Aram Mikaelian}
\thanks{Supported by  EPSRC grant EP/D077656/1}

\begin{document}
\begin{abstract}
We compute the cohomology $H^*(\cH,k)=\Ext^*_\cH(k,k)$ 
where $\cH=\cH(n,q)$ is the Hecke algebra
of the symmetric group $\fS_n$ at a primitive $\ell$th 
root of unity $q$, and $k$ is a field of characteristic zero.
The answer is particularly interesting when $\ell=2$,
which is the only case where it is not graded commutative.
We also carry out the corresponding computation for Hecke algebras
of type $B_n$ and $D_n$ when $\ell$ is odd.
\end{abstract}