Chern character

Summary

The Chern character is a ring homomorphism from K-theory to rational cohomology, or to the rational Chow ring in algebraic geometry. It is built from the Chern classes so that a line bundle $L$ goes to $e^{c_1(L)}$. Unlike the total Chern class, it turns direct sums into sums and tensor products into products. It appears in the Grothendieck–Riemann–Roch theorem and the Atiyah–Singer index theorem.