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On the Riemann-Roch formula without projective hypothesis
Citation
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 |
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| Author/s: |
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| 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 |
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 |
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| 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 |
