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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

##### MSC:
 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 14G25 Global ground fields in algebraic geometry 14C05 Parametrization (Chow and Hilbert schemes)
##### Keywords:
arithmetic variety; Chow group; hermitian bundle