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 diagonalizable 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 fiber, 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 Tang (Math. Z. 290 (2018) 307–346) 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 Köhler and Roessler (Invent. Math. 145 (2001) 333–396).

中文翻译：

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算术Lefschetz–Riemann–Roch定理

在本文中，我们考虑在Arakelov几何背景下的常规射影算术方案，其中的任何一种都具有与有限循环组相关联的对角化组方案的作用，并且具有等变的，非常充足的可反转层。对于这样的算术方案之间的任何等变态，这在通用光纤上都是平滑的，我们定义了相应的更高等变算术K群之间的直接图像图，并讨论了其传递性。然后，我们使用在Tang（Math。Z。290（2018）307–346）证明了算术Lefschetz-Riemann-Roch定理。该定理可以被看作是一个一般化，较高等变算术K理论，由Kohler和Roessler的证明莱夫谢茨类型的定点式（发明。数学。145（2001）333-396）。