lichtenbaum conjectured that special values of the zeta function of a number field could be expressed in terms of the "k"-groups of the ring of integers of the field. these special values were known to be related to the étale cohomology of the ring of integers. quillen therefore generalized lichtenbaum's conjecture, predicting the existence of a spectral sequence like the atiyah–hirzebruch spectral sequence in topological "k"-theory. quillen's proposed spectral sequence would start from the étale cohomology of a ring "r" and, in high enough degrees and after completing at a prime formula_13 invertible in "r", abut to the formula_13-adic completion of the "k"-theory of "r". in the case studied by lichtenbaum, the spectral sequence would degenerate, yielding lichtenbaum's conjecture.