arXiv:1207.4078 A commutative P^1-spectrum representing motivic cohomology over Dedekind domains I fra arXiv Front: math.AT av Markus Spitzweck We construct a motivic Eilenberg-MacLane spectrum with a highly structured multiplication over smooth schemes over Dedekind domains which represents Levine’s motivic cohomology. The latter is defined via Bloch’s cycle complexes. Our method is by gluing p-completed and rational parts along an arithmetic square. Hereby the finite coefficient spectra are obtained by truncated etale sheaves (relying on the now proven Bloch-Kato conjecture) and a variant of Geisser’s version of syntomic cohomology, and the rational spectra are the ones which represent Beilinson motivic cohomology. As application the arithmetic motivic cohomology groups can be realized as Ext-groups in a triangulated category of Tate sheaves with integral coefficients. These can be modelled as representations of derived fundamental groups.
nLab page on Motivic cohomology temp