Motivic E_{infinity} algebras and the motivic dga

Abstract

In this paper we define an explicit E_{infinity}-structure, i.e. a coherently homotopy associative and commutative product on chain complexes defining (integral and mod-l) motivic cohomology as well as mod -l \'etale cohomology. We also discuss several applications. In addition, our constructions show that the source of the E_{\infinity}-structure on the motivic complexes provided with the pairing defined by Suslin and Voevodsky is not chain-theoretic as is the case for the singular co-chain complexes for topological spaces.