Geodesic
Topological Cyclic Homology Via the Norm
Documenta mathematica, Tome 23 (2018), pp. 2101-2163.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 $C_n$-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 $TC$.
Classification : 55P91, 19D55, 16E40
Keywords: topological cyclic homology, multiplicative norm, cyclotomic spectrum, Adams operations 
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     author = {Angeltveit, Vigleik and Blumberg, Andrew J. and Gerhardt, Teena and Hill, Michael A. and Lawson, Tyler and Mandell, Michael A.},
     title = {Topological {Cyclic} {Homology} {Via} the {Norm}},
     journal = {Documenta mathematica},
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     volume = {23},
     year = {2018},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a1/}
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Angeltveit, Vigleik; Blumberg, Andrew J.; Gerhardt, Teena; Hill, Michael A.; Lawson, Tyler; Mandell, Michael A. Topological Cyclic Homology Via the Norm. Documenta mathematica, Tome 23 (2018), pp. 2101-2163. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a1/