Gillet, Henri; Soulé, Christophe Un théorème de Riemann-Roch-Grothendieck arithmétique. (An arithmetic Riemann-Roch-Grothendieck theorem). (French) Zbl 0732.14002 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. Cited in 2 ReviewsCited in 5 Documents 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 PDF BibTeX XML Cite \textit{H. Gillet} and \textit{C. Soulé}, C. R. Acad. Sci., Paris, Sér. I 309, No. 17, 929--932 (1989; Zbl 0732.14002) OpenURL