A technical conjecture which connects algebraic K-theory to étale cohomology. The conjecture was made more precise by Dwyer and Friedlander (1982). Thomason (1985) established the first half of this conjecture, but the entire conjecture has not yet been established.
Quillen-Lichtenbaum Conjecture
References
Dwyer, W. and Friedlander, E. "Étale
-Theory and Arithmetic." Bull. Amer. Math. Soc. 6,
453-455, 1982.Lichtenbaum, S. Values of Zeta Functions, Étale
Cohomology and Algebraic 
-Theory. New York:Springer-Verlag, 1973.Lichtenbaum,
S. "On the Values of Zeta and 
-Functions: I." Ann. Math. 96, 338-360,
1972.Snaith, V. "Unitary 
-Homology and the Lichtenbaum-Quillen Conjecture on the Algebraic
-Theory
of Schemes." In Algebraic
Topology, Aarhus 1982: Proceedings of a Conference Held at the Mathematics Institute,
Aarhus University, Aarhus, August 1-7, 1982 (Ed. I. Madsen and B. Oliver).
Berlin:Springer-Verlag, pp. 128-155, 1984.Thomason, R. W.
"Algebraic 
-Theory and Étale Cohomology." Ann. Sci. École
Norm. Sup. 18, 437-552, 1985.Weibel, C. A. "The
Mathematical Enterprises of Robert Thomason." Bull. Amer. Math. Soc. 34,
1-13, 1996.
Cite this as:
Weisstein, Eric W. "Quillen-Lichtenbaum Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Quillen-LichtenbaumConjecture.html