The cyclotomic trace and curves on K-theory

@article{Betley2005TheCT,
  title={The cyclotomic trace and curves on K-theory},
  author={S. Betley and C. Schlichtkrull},
  journal={Topology},
  year={2005},
  volume={44},
  pages={845-874}
}
We give a functorial description of the topological cyclic homology of a ring A in terms of the relative algebraic K-theory of the truncated polynomial rings An=A[x]/xn. This description involves the projection and transfer maps relating the relative K-theory spectra K˜(An) when n varies. From this point of view the cyclotomic trace corresponds to multiplication by the units 1+x+⋯+xn-1 in K˜1(Z[x]/xn). 
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