An arithmetic Lefschetz-Riemann-Roch theorem. With an appendix by Xiaonan Ma
| Autor: | Tang, Shun |
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| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/plms.12349 |
| Popis: | In this article, we consider regular projective arithmetic schemes in the context of Arakelov geometry, any of which is endowed with an action of the diagonalisable group scheme associated to a finite cyclic group and with an equivariant very ample invertible sheaf. For any equivariant morphism between such arithmetic schemes, which is smooth over the generic fibre, we define a direct image map between corresponding higher equivariant arithmetic K-groups and we discuss its transitivity property. Then we use the localization sequence of higher arithmetic K-groups and the higher arithmetic concentration theorem developed in \cite{T3} to prove an arithmetic Lefschetz-Riemann-Roch theorem. This theorem can be viewed as a generalization, to the higher equivariant arithmetic K-theory, of the fixed point formula of Lefschetz type proved by K. K\"{o}hler and D. Roessler in \cite{KR1}. Comment: 65 pages, published version |
| Databáze: | arXiv |
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