Chern class and Riemann-Roch theorem for cohomology theory without homotopy invariance

Abstract

In this paper, we formulate axioms of certain graded cohomology theory for which Chern class maps from higher K-theory are defined, following the method of Gillet [Gi1]. We will not include homotopy invariance nor purity in our axioms. It will turn out that the Grothendieck-Riemann-Roch theorem and the Riemann-Roch theorem without denominators hold for our higher Chern classes. We will also give two applications of our Riemann-Roch results.

64 pages. Appendix B by Kei Hagihara has been added. Subsection A.1 and Proposition A.7 has been added

Cited by in corpus (4)

• CM periods, CM regulators and hypergeometric functions, I
• The slice spectral sequence for singular schemes and applications
• A formula for Beilinson's regulator map on K_1 of a fibration of curves having a totally degenerate semistable fiber
• Real Regulator on K_1 of elliptic surfaces