Definition 82.28.2. In Situation 82.2.1 let $X/B$ be good. Let $\mathcal{E}$ be a finite locally free sheaf of rank $r$ on $X$. For $i = 0, \ldots , r$ the *$i$th Chern class of $\mathcal{E}$* is the bivariant class $c_ i(\mathcal{E}) \in A^ i(X)$ of degree $i$ constructed in Lemma 82.28.1. The *total Chern class of $\mathcal{E}$* is the formal sum

which is viewed as a nonhomogeneous bivariant class on $X$.

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