Cyclic homology, Serre's local factors and the -operations

Abstract

We show that for a smooth, projective variety X defined over a number field K, cyclic homology with coefficients in the ringA∞ = Q ν|∞ Kν, provides the right theory to obtain, using the λ-operations, Serre’s archimedean local factors of the complex Lfunction of X as regularized determinants. Contents