Geodesic
Topological Cyclic Homology Via the Norm
Documenta mathematica, Tome 23 (2018), pp. 2101-2163
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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 Bökstedt coherence machinery. We are also able to define two relative versions of topological cyclic homology (TC) and TR-theory: one starting with a ring Cn​-spectrum and one starting with an algebra over a cyclotomic commutative ring spectrum A. We describe spectral sequences computing the relative theory over A 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.
DOI : 10.4171/dm/671
Classification : 16E40, 19D55, 55P91
Mots-clés : Adams operations, topological cyclic homology, multiplicative norm, cyclotomic spectrum 
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     author = {Vigleik Angeltveit and Andrew J. Blumberg and Teena Gerhardt and Michael A. Hill and Tyler Lawson and Michael A. Mandell},
     title = {Topological {Cyclic} {Homology} {Via} the {Norm}},
     journal = {Documenta mathematica},
     pages = {2101--2163},
     year = {2018},
     volume = {23},
     doi = {10.4171/dm/671},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/671/}
}
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Vigleik Angeltveit; Andrew J. Blumberg; Teena Gerhardt; Michael A. Hill; Tyler Lawson; Michael A. Mandell. Topological Cyclic Homology Via the Norm. Documenta mathematica, Tome 23 (2018), pp. 2101-2163. doi: 10.4171/dm/671

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