Inverting the Motivic Bott Element

LEVINE, MARC

Department of Mathematics, Northeastern University, Boston, MA 02115, U.S.A. e-mail: [email protected]

K-Theory 19(1):p 1-28, January 2000.

We prove a version for motivic cohomology of Thomason's theorem on Bott-periodic K-theory, namely, that for a field k containing the nth roots of unity, the mod n motivic cohomology of a smooth k-scheme agrees with mod n étale cohomology, after inverting the element in H⁰(k,Z/n(1)) corresponding to a primitive nth root of unity.