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Classes caractéristiques en théorie d’Arakelov. (Characteristic classes in Arakelov theory). (French) Zbl 0613.14007
This paper is a continuation of the authors’ paper in C. R. Acad. Sci., Paris, Sér. I 299, 563-566 (1984; Zbl 0607.14003). Let X be an arithmetic variety, i.e. a scheme which is regular and quasi-projective over \({\mathbb{Z}}\) such that the generic fiber \(X_{{\mathbb{Q}}}\) is projective over \({\mathbb{Q}}\). The authors construct a Chow group on X with a graded \({\mathbb{Q}}\)-algebra structure, \(CH(X)_{{\mathbb{Q}}}\). A hermitian bundle on X is given by \(\bar E=(E,h)\), where E is a locally free \({\mathcal O}_ X\)- module and h a hermitian metric on the holomorphic bundle \(E({\mathbb{C}})\) invariant under the involution of X(\({\mathbb{C}})\) induced by complex conjugation. The authors define characteristic classes in \(CH(X)_{{\mathbb{Q}}}\) of certain polynomial expressions of \(\bar E\).
Reviewer: A.Papantonopoulou

14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
14G25 Global ground fields in algebraic geometry
14C05 Parametrization (Chow and Hilbert schemes)