the necessity of localizing at a prime formula_13 suggested to browder that there should be a variant of "k"-theory with finite coefficients. he introduced "k"-theory groups "k"("r"; z/formula_13z) which were z/formula_13z-vector spaces, and he found an analog of the bott element in topological "k"-theory. soule used this theory to construct "étale chern classes", an analog of topological chern classes which took elements of algebraic "k"-theory to classes in étale cohomology. unlike algebraic "k"-theory, étale cohomology is highly computable, so étale chern classes provided an effective tool for detecting the existence of elements in "k"-theory. william g. dwyer and eric friedlander then invented an analog of "k"-theory for the étale topology called étale "k"-theory. for varieties defined over the complex numbers, étale "k"-theory is isomorphic to topological "k"-theory. moreover, étale "k"-theory admitted a spectral sequence similar to the one conjectured by quillen. thomason proved around 1980 that after inverting the bott element, algebraic "k"-theory with finite coefficients became isomorphic to étale "k"-theory.