Un théorème de Riemann-Roch-Grothendieck arithmétique. (An arithmetic Riemann-Roch-Grothendieck theorem). (French) Zbl 0732.14002

Gillet, Henri; Soulé, Christophe

C. R. Acad. Sci., Paris, Sér. I 309, No. 17, 929-932 (1989).

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

Keywords:

Riemann-Roch-Grothendieck theorem; Arakelov geometry; determinant line bundle; Quillen metric