Definition 9.4.16 (Chern character). The Chern character is the stable multiplicative cohomology operation induced by the composite \[ \KU \longrightarrow \KU _{\Q }\xrightarrow {\ \simeq \ }H\Q [\beta ^{\pm 1}], \] where the second map is the inverse of the isomorphism in Proposition 9.4.15. Thus, for every anima \(X\) and every \(k\in \Z \), it gives a natural morphism \[ \mathrm {ch}\colon \KU ^k(X)\longrightarrow \prod _{n\in \Z }H^{k+2n}(X;\Q ). \]
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