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Un théorème de Riemann-Roch-Grothendieck arithmétique. (An arithmetic Riemann-Roch-Grothendieck theorem). (French) Zbl 0732.14002
Summary: We obtain a Riemann-Roch-Grothendieck theorem in Arakelov geometry which computes the determinant line bundle of the cohomology of a hermitian algebraic vector bundle, equipped with the Quillen metric. The result is valid for any proper and generically smooth morphism between arithmetic varieties.

MSC:
14C40 Riemann-Roch theorems
14G40 Arithmetic varieties and schemes; Arakelov theory; heights
14M12 Determinantal varieties
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