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A chain morphism for Adams operations on rational algebraic K-theory

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For any regular noetherian scheme X and every k ≥ 1, we define a chain morphism ψk between two chain complexes whose homology with rational coefficients is isomorphic to the algebraic K-groups of X tensored by ℚ. It is shown that the morphisms ψk induce in homology the Adams operations defined by Gillet and Soulé or the ones defined by Grayson.

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3. P. Deligne , Le déterminant de la cohomologie, Current trends in arithmetical algebraic geometry (Arcata, Calif., 1985), Contemp. Math. 67, Amer. Math. Soc., Providence, RI, 1987, pp. 93177.

12. C. Soulé , Lectures on Arakelov geometry, Cambridge Studies in Advanced Mathematics 33, Cambridge University Press, Cambridge, 1992, With the collaboration of D. Abramovich, J.-F. Burnol and J. Kramer.

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Journal of K-Theory
  • ISSN: 1865-2433
  • EISSN: 1865-5394
  • URL: /core/journals/journal-of-k-theory
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