On the Riemann-Roch formula without projective hypothesis

Navarro Garmendia, Alberto and Navarro Garmendia, José (2020). On the Riemann-Roch formula without projective hypothesis. "Transactions of the American Mathematical Society", v. 374 (n. 2); pp. 755-772. ISSN 0002-9947. https://doi.org/10.1090/tran/8107.

Description

Title: On the Riemann-Roch formula without projective hypothesis
Author/s:
  • Navarro Garmendia, Alberto
  • Navarro Garmendia, José
Item Type: Article
Título de Revista/Publicación: Transactions of the American Mathematical Society
Date: 3 November 2020
ISSN: 0002-9947
Volume: 374
Subjects:
Faculty: E.T.S. Arquitectura (UPM)
Department: Matemática Aplicada
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Let S be a finite dimensional noetherian scheme. For any proper morphism between smooth S-schemes, we prove a Riemann-Roch formula relating higher algebraic K-theory and motivic cohomology, thus with no projective hypothesis neither on the schemes nor on the morphism. We also prove, without projective assumptions, an arithmetic Riemann-Roch theorem involving Arakelov?s higher K-theory and motivic cohomology as well as an analogue result for the relative cohomology of a morphism. These results are obtained as corollaries of a motivic statement that is valid for morphisms between oriented absolute spectra in the stable homotopy category of S.

More information

Item ID: 67845
DC Identifier: https://oa.upm.es/67845/
OAI Identifier: oai:oa.upm.es:67845
DOI: 10.1090/tran/8107
Official URL: https://www.ams.org/journals/tran/2021-374-02/S0002-9947-2020-08107-0/
Deposited by: Memoria Investigacion
Deposited on: 03 Sep 2021 05:47
Last Modified: 03 Sep 2021 05:47
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