• Corpus ID: 50623237

Topological cyclic homology via the norm

  title={Topological cyclic homology via the norm},
  author={Vigleik Angeltveit and Andrew J. Blumberg and Teena Gerhardt and Matthew Hill and Tyler Lawson and Michael A. Mandell},
  journal={arXiv: K-Theory and Homology},
We describe a construction of the cyclotomic structure on topological Hochschild homology ($THH$) of a ring spectrum using the Hill-Hopkins-Ravenel multiplicative norm. Our analysis takes place entirely in the category of equivariant orthogonal spectra, avoiding use of the Bokstedt coherence machinery. We are able to define versions of topological cyclic homology ($TC$) and TR-theory relative to a cyclotomic commutative ring spectrum $A$. We describe spectral sequences computing this relative… 

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