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Fix target groups for chern class construction
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aisejohan committed Mar 2, 2023
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Expand Up @@ -9181,12 +9181,12 @@ \section{Chern classes and the derived category}
such that $Lf^*E$ is isomorphic in $D(\mathcal{O}_Y)$
to a locally bounded complex $\mathcal{E}^\bullet$ of finite locally free
$\mathcal{O}_Y$-modules. Then there exists unique bivariant classes
$c(E) \in A^*(X)$, $ch(E) \in A^*(X) \otimes \mathbf{Q}$, and
$c(E) \in \prod_{p \geq 0} A^p(X)$,
$ch(E) \in \prod_{p \geq 0} A^p(X) \otimes \mathbf{Q}$, and
$P_p(E) \in A^p(X)$, independent of the choice of $f : Y \to X$
and $\mathcal{E}^\bullet$, such that the restriction of these classes
to $Y$ are equal to $c(\mathcal{E}^\bullet) \in A^*(Y)$,
$ch(\mathcal{E}^\bullet) \in A^*(Y) \otimes \mathbf{Q}$, and
$P_p(\mathcal{E}^\bullet) \in A^p(Y)$.
to $Y$ are equal to $c(\mathcal{E}^\bullet)$,
$ch(\mathcal{E}^\bullet)$, and $P_p(\mathcal{E}^\bullet)$.
\end{lemma}

\begin{proof}
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