universal algebra Algebraic theories
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Dennis trace is a natural morphism from algebraic K-theory of rings to Hochschild homology
K ( − ) ⟶ THH ( − ) .
K(-) \longrightarrow THH(-)
While various versions of
Chern character are maps from K-theory to some (co)homology of a space, algebra, scheme, the Dennis trace map underlies this phenomenon at the more fundamental level of K-theory space.
The Dennis trace lifts to to
ring spectra and as such factors through the map ]] from TC ( − ) ⟶ THH ( − ) TC(-) \longrightarrow THH(-) topological cyclic homology, this lift is called the . cyclotomic trace Literature
Ib Madsen, Algebraic K-theory and traces, Current Developments in Mathematics, 1995.
John Rognes, after Marcel Bökstedt, Trace maps from the algebraic K-theory of the integers, K-theory archive
M. R. Kantorovitz,
Adams operations and the Dennis trace map, JPAA 144, 1 (Dec 1999), 21-27 [doi]
M. R. Kantorovitz, C. Miller,
An explicit description of the Dennis trace map, claudia-revised.ps
Andrew Blumberg, David Gepner, Goncalo Tabuada, Uniqueness of the multiplicative cyclotomic trace ( arXiv:1103.3923)
Bjørn Dundas, Thomas Goodwillie, Randy McCarthy, The local structure of algebraic K-theory, Springer 2013
Revised on November 6, 2015 16:11:42