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

Published online by Cambridge University Press:  25 July 2014

Alain Connes  and
Caterina Consani
Alain Connes
Affiliation:
Collège de France, 3 rue d'Ulm, Paris F-75005, France, I.H.E.S. and Ohio State University, alain@connes.org
Caterina Consani
Affiliation:
Department of Mathematics, The Johns Hopkins University, Baltimore, MD 21218, kc@math.jhu.edu
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Abstract

We show that for a smooth, projective variety X defined over a number field K, cyclic homology with coefficients in the ring , provides the right theory to obtain, using λ-operations, Serre's archimedean local factors of the complex L-function of X as regularized determinants.

Keywords

Cyclic homologyDeligne cohomologyGamma factorscomplex L-functionmotives16E4011G4013D311G0914F25

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Type
Research Article
Information
Journal of K-Theory , Volume 14 , Issue 1 , August 2014 , pp. 1 - 45
Copyright
Copyright © ISOPP 2014 

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