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Mathematics, K-Theory and Homology, Algebraic Geometry, Algebraic Topology, Category Theory
Abstract:
In this paper we prove a categorification of the Grothendieck-Riemann-Roch
theorem. Our result implies in particular a Grothendieck-Riemann-Roch theorem
for To\"en and Vezzosi's secondary Chern character. As a main application, we
establish a comparison between the To\"en-Vezzosi Chern character and the
classical Chern character, and show that the categorified Chern character
recovers the classical de Rham realization.
