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The Stacks project

Definition 42.38.8. Let (S, \delta ) be as in Situation 42.7.1. Let X be locally of finite type over S. Let \mathcal{E} be a locally free \mathcal{O}_ X-module of rank r. For i = 0, \ldots , r the ith Chern class of \mathcal{E} is the bivariant class c_ i(\mathcal{E}) \in A^ i(X) of degree i constructed in Lemma 42.38.7. The total Chern class of \mathcal{E} is the formal sum

c(\mathcal{E}) = c_0(\mathcal{E}) + c_1(\mathcal{E}) + \ldots + c_ r(\mathcal{E})

which is viewed as a nonhomogeneous bivariant class on X.


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