Holmstrom Etale K-theory

Etale K-theory

A reduction map? (Article by G. Banaszak, W. Gajda, B. Kahn, and P. Krason)


Etale K-theory

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.”


Etale K-theory

Mitchell

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.


Etale K-theory

Soulé: Operations on etale K-theory. Applications. In LNM 966 (1982).


Etale K-theory

MathSciNet

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Google

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category: Search results


Etale K-theory

AG (Algebraic geometry)

category: World [private]


Etale K-theory

Kth

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Etale K-theory

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.


Etale K-theory

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

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Etale K-theory

A book by Jardine

R. W. Thomason, Survey of algebraic vs. étale topological KK-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???

category: Paper References

nLab page on Etale K-theory

Created on June 10, 2014 at 21:14:54 by Andreas Holmström