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

Masanori Asakura; Kanetomo Sato

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arXiv · 1301.5829

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

Masanori Asakura·Kanetomo Sato

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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.

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BibTeX RIS

Masanori Asakura, Kanetomo Sato. 2013-01-24. Chern class and Riemann-Roch theorem for cohomology theory without homotopy invariance. https://arxiv.org/abs/1301.5829

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