Some remarks concerning mod-n K-theory, by Eric M. Friedlander and Mark E. Walker

The purpose of this short paper is to draw two conclusions concerning mod-n algebraic K-theory of smooth, quasi-projective varieties over an algebraically closed field by comparing this spectral sequence to its "localization" which we show converges to mod-n etale K-theory. We verify that the map from mod-n algebraic K-theory to mod-n etale K-theory of a smooth quasi-projective variety X over an algebraically closed field in which n is invertible is surjective in degrees greater than or equal to twice the dimension of X. We show that certain projective smooth 3-folds X constructed by S. Bloch and H. Esnault have non-zero elements in K_0 of X with mod-n coefficients but which are killed by multiplication by a sufficiently high power of the Bott element.

Eric M. Friedlander <>
Mark E. Walker <>