The Motivic DGA, by Roy Joshua

In this paper, we associate to each smooth quasi-projective scheme over a field, an E-infinity differential graded algebra whose cohomology groups are the motivic cohomology groups of the scheme. Such a construction is known currently only for the case the scheme itself is a field. By standard arguments, modulo torsion, we also produce a strictly commutative differential graded algebra associated to the above E-infinity differential graded algebra. This is the motivic dga. Using this, we provide a construction of a category of relative mixed Tate motives for any linear smooth projective variety over a field. We also obtain certain cohomology operations in mod-p motivic cohomology.

Roy Joshua <>