Etale Ktheory

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.\ 393443) (1987, some proceedings)
There are also earlier papers by Thomason et al on etale Ktheory, but then often called just topological Ktheory. There are three: RiemannRoch for algebraic vs topological Ktheory, Algebraic Ktheory eventually surjects onto topological Ktheory, The LichtenbaumQuillen 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 Ktheory 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 Semistable Conjecture of Jannsen and Fontaine (proved before by Tsuji and Faltings) is true for projective vertical fine and saturated logsmooth families with reduction of Cartier type. We derive it from Thomason's comparison theorem between algebraic and etale Ktheories."
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Some Research Articles
On the Ktheory 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^vcoefficients, the cyclotomic trace induces an isomorphism of the DwyerFriedlander etale Ktheory of X and the topological cyclic homology of X.
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