\begin{center} \emph{{\bf Weight conjectures for Ordinary Characters}\\ 
                       Geoffrey R. Robinson\\ 
                       School of Mathematics and Statistics\\ 
                       University of Birmingham\\
                       Edgbaston\\ 
                       Birmingham B15 2TT\\ England\\
                       Fax UK 121 4143389\\}


\end{center}

\bigskip
\noindent{\bf INTRODUCTION:} When $p$ is a prime, Dade's Projective 
Conjecture (DPC) for a $p$-block $B$ whose defect group is non-central
gives an alternating sum which (conjecturally) expresses the number 
of irreducible  characters of defect $d$ in $B$ lying over a 
linear character $\lambda$ of a central $p$-subgroup $Z$ 
( denoted $k_{d}(B,\lambda)$)  in terms of an alternating sum whose 
terms can all be calculated $p$-locally. This conjecture is a refinement 
of the Kn\"orr-Robinson formulation ( see [8]) of Alperin's Weight 
Conjecture (AWC) ( see [1] ). DPC is only formulated for finite groups 
$G$ such that $O_{p}(G) \leq Z(G),$ and for $p$-blocks of $G$ whose 
defect group(s) strictly contain $O_{p}(G).$ We will give a precise 
statement of this conjecture later.