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\begin{center}
  {\Large Corrections for 
 W. Soergel: Langland's philosophy and Koszul duality, pp. 379--414
 in the  Proceedings of NATO ASI 2000 in Constanta
of a conference on Algebra-Representation Theory,
edited by Roggenkamp and Stefanescu, published by Kluwer
 (2001)}
\end{center}
The argument on page 405 at the top needs fixing.
This is still a fix on the quick.
First we treat the case that $\mathcal F = i_{n!} \underline{B/B}$ is
the skyscraper at the one-point cell.
In this case the claim follows from the fact that $i_{n!} i_n^! \mathcal E \rightarrow
\mathcal E$ induces an injection on hypercohomology, which follows from the degeneration of
the spectral sequence computing $\mathbb H^\bullet \mathcal E$.
Then, for the general case, it will be sufficient to check the commutativity of the
following diagrams, for $\mathcal A \in \mathcal D (G/P_s)$ and $\mathcal F \in \mathcal D (G/B):$
\begin{displaymath}
 \xymatrix{
\op{Hom}_{\mathcal D} (\pi^\ast \mathcal A, \mathcal F)\ar[d]^-{\wr} \ar[r]& \op{Hom} (\mathbb H^\bullet
\pi^\ast \mathcal A, \mathbb H^\bullet \mathcal F)\ar[d]\\
\op{Hom}_{\mathcal D} (\mathcal A, \pi_\ast \mathcal F) \ar[r] & \op{Hom} (\mathbb H^\bullet \mathcal A,
\mathbb H^\bullet \pi_\ast \mathcal F)
}
\end{displaymath}
for the map on the right
 coming from $\mathcal A \rightarrow \pi_\ast\pi^\ast \mathcal A$,
and
\begin{displaymath}
 \xymatrix{
\op{Hom}_{\mathcal D} (\mathcal F, \pi^!\mathcal A) \ar[r]\ar[d]^-{\wr} & \op{Hom}_C (\mathbb H^\bullet
\mathcal F, \mathbb H^\bullet \pi^! \mathcal A) \ar[d]^-{\wr}\\
\op{Hom}_{\mathcal D} (\pi_! \mathcal F, \mathcal A) \ar[r] & \op{Hom}_{C^s} (\mathbb H^\bullet \pi_! \mathcal F,
\mathbb H^\bullet \mathcal A)
}
\end{displaymath}
Here the point is to construct dually  a canonical isomorphism
$\op{Hom}_{C^s}(C,\mathbb H^\bullet \mathcal A)\sira \mathbb H^\bullet\pi^!
\mathcal A$ and show that the resulting diagram will commute.
With these diagrams, a non-injective case  would lead
 to a noninjective case with
$\mathcal F$ the skyscraper, which we have already shown to be impossible.
\\[3mm]\noindent
It now seems to me as if before 4.2.3 we should rather ask
$\mathcal M^x=i_\ast \tau[\op{dim}Y]$ and in 4.2.3
correspondingly $\op{hom}_{\mathcal D}(L^x, M^x)
\neq 0$. Furthermore it seems as if in 4.2.4 we
should ask $\op{hom}_{\mathcal D}(L_x, N_x)\neq 0$.

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