A reduction map? (Article by G. Banaszak, W. Gajda, B. Kahn, and P. Krason)
http://www.math.uiuc.edu/K-theory/0300: Niziol: “We show that, for odd primes, the Semi-stable Conjecture of Jannsen and Fontaine (proved before by Tsuji and Faltings) is true for projective vertical fine and saturated log-smooth families with reduction of Cartier type. We derive it from Thomason’s comparison theorem between algebraic and etale K-theories.”
On the K-theory and topological cyclic homology of smooth schemes over a discrete valuation ring, by Thomas Geisser and Lars Hesselholt: Let V be a discrete valuation ring of mixed characteristic (0,p) and let X be a smooth and proper scheme over V. We show that with Z/p^v-coefficients, the cyclotomic trace induces an isomorphism of the Dwyer-Friedlander etale K-theory of X and the topological cyclic homology of X.
Soulé: Operations on etale K-theory. Applications. In LNM 966 (1982).
arXiv: Experimental full text search
AG (Algebraic geometry)
Kth
Gillet in review of Friedlander’s first paper says that the theory is defined for simplicial schemes, or pairs of simplicial schemes. See the review for details about the base.
Dwyer and Friedlander: Algebraic and etale K-theory (1985)
See perhaps also Thomason’s great paper.
Dwyer and Friedlander: Etale K-theory of Azumaya algebras
I am quite confused about the terms topological K-theory, topological K-cohomology, etale K-theory, and topological K-homology. Is it the case that Thomason uses topological K-theory for what is otherwise called etale K-theory??? See his paper Riemann-Roch for algebraic vs topological K-theory, see maybe also modern papers by Rognes, Ausoni and maybe others. See for example the review http://www.ams.org/mathscinet-getitem?mr=662604
R. W. Thomason, Survey of algebraic vs. étale topological -theory (pp.\ 393–443) (1987, some proceedings)
There are also earlier papers by Thomason et al on etale K-theory, but then often called just topological K-theory. There are three: Riemann-Roch for algebraic vs topological K-theory, Algebraic K-theory eventually surjects onto topological K-theory, The Lichtenbaum-Quillen conjecture for … http://www.ams.org/mathscinet-getitem?mr=686114. However, I think the best starting point might be the survey, and then look at these older papers if details are needed.
Friedlander: Etale K-theory I (1980) http://www.ams.org/mathscinet-getitem?mr=0586424. See also later papers by Friedlander/Dwyer. Maybe papers by Soule???
nLab page on Etale K-theory