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.
ReferencesDwyer, 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