A LEFSCHETZ FIXED-POINT THEOREM IN ARAKEL OV GEOMETRY

We consider arithmetic varieties endowed with an action of the group s cheme of n-th roots of unity and we define equivariant arithmetic K-0- theory for these varieties. We then state a Riemann-Roch theorem for t he natural transformation of equivariant arithmetic K-0-theory induced by the restriction to the fixed point scheme and we show that it impl ies a version of Bismut's conjecture of an equivariant arithmetic Riem ann-Roch theorem. (C) Academie des Sciences/Elsevier, Paris.