Etale K-theory
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General Introduction
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Search results
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Online References
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Paper References
R. W. Thomason, Survey of algebraic vs. étale topological $K$-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 ... MR686114. 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) MR0586424. See also later papers by Friedlander/Dwyer. Maybe papers by Soulé???
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
K0300: 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."
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Some Research Articles
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.
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Other Information
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