The categorified Grothendieck-Riemann-Roch theorem

Marc Hoyois, Pavel Safronov, Sarah Scherotzke, Nicolò Sibilla

Research output: Contribution to journalArticlepeer-review

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 Toën and Vezzosi's secondary Chern character. As a main application, we establish a comparison between the Toën-Vezzosi Chern character and the classical Chern character, and show that the categorified Chern character recovers the classical de Rham realization.
Original languageEnglish
Number of pages58
JournalCompositio Mathematica
Publication statusAccepted/In press - 19 Aug 2020

Keywords

  • 14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry
  • 19D55 K-theory and homology; cyclic homology and cohomology

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