### 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 <joshua@math.ohio-state.edu>