Abstract
This paper reviews the relations between algebraic K-theory and topological cyclic homology given by cyclotomic trace. If one, very superficially, views algebraic K-theory as classifying invertible matrices, then the cyclotomic trace records the trace of all powers of matrices. In a more relevant formulation, the topological cyclic homology has the same relationship to Bökstedt’s topological Hochschild homology as Connes’ cyclic homology has to Hochschild homology, and the cyclotomic trace is a topological cyclic version of the Dennis trace map.
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© 1994 Birkhäuser Verlag
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Madsen, I. (1994). The Cyclotomic Trace in Algebraic K-Theory. In: Joseph, A., Mignot, F., Murat, F., Prum, B., Rentschler, R. (eds) First European Congress of Mathematics Paris, July 6–10, 1992. Progress in Mathematics, vol 120. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9112-7_9
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DOI: https://doi.org/10.1007/978-3-0348-9112-7_9
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