2022-01-20T07:53:19Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000548852021-03-01T10:08:16ZChern Class and Riemann-Roch Theorem for Cohomology Theory without Homotopy InvarianceAsakura Masanori163303Sato, Kanetomo163304Hagihara, Kei163305$K$-theorycohomology theoryChern classRiemann-Roch theoremIn this paper, we formulate axioms of certain graded cohomology theory and define higher Chern class maps following the method of Gillet [Gi1]. We will not include homotopy invariance nor purity in our axioms. It will turn out that the Riemann-Roch theorem without denominators holds for our higher Chern classes. We will give two applications of our Riemann-Roch results in $\S\S11-13$.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2019-12-20application/pdfJournal of Mathematical Sciences The University of Tokyo326249334AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/54885/files/jms260301.pdfeng