Topological cyclic homology via the norm
Abstract
We describe a construction of the cyclotomic structure on topological Hochschild homology ($THH$) of a ring spectrum using the HillHopkinsRavenel multiplicative norm. Our analysis takes place entirely in the category of equivariant orthogonal spectra, avoiding use of the Bökstedt coherence machinery. We are able to define versions of topological cyclic homology ($TC$) and TRtheory relative to a cyclotomic commutative ring spectrum $A$. We describe spectral sequences computing this relative theory $_ATR$ in terms of $TR$ over the sphere spectrum and vice versa. Furthermore, our construction permits a straightforward definition of the Adams operations on $TR$ and $TC$.
 Publication:

arXiv eprints
 Pub Date:
 January 2014
 arXiv:
 arXiv:1401.5001
 Bibcode:
 2014arXiv1401.5001A
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematics  Algebraic Topology
 EPrint:
 Revised draft. Error about cyclotomic structure on relative THH for general A corrected