From cfe392885a48fff6d60541076d841602f04f2389 Mon Sep 17 00:00:00 2001 From: Aise Johan de Jong Date: Thu, 2 Mar 2023 17:48:58 -0500 Subject: [PATCH] Fix target groups for chern class construction THanks to 11k https://stacks.math.columbia.edu/tag/0GUD#comment-7944 --- chow.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/chow.tex b/chow.tex index 4f075c8ba..ffeb2ec95 100644 --- a/chow.tex +++ b/chow.tex @@ -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}