Remark 42.56.5. Let (S, \delta ) be as in Situation 42.7.1. Let X be locally of finite type over S. The Chern character map defines a canonical ring map
ch : K_0(\textit{Vect}(X)) \longrightarrow \prod \nolimits _{i \geq 0} A^ i(X) \otimes \mathbf{Q}
by sending a generator [\mathcal{E}] on the left hand side to ch(\mathcal{E}) and extending additively. This is well defined by Lemma 42.45.2 and a ring homomorphism by Lemma 42.45.3.
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