Holmstrom Representability in algebraic geometry

See notes by Deligne/Voevodsky for a proof of the fact that the Eilenberg-MacLane spectrum represents motivic cohomology.

The etale preprint of Quick

The preprint of Jardine treating abstract representability theorems for stable model cats

Hornbostel on hermitian K-theory and Witt groups

Possibly the following fact is of interest: The contravariant functor from $Sm_k$ to Huber’s triangulated tensor category of mixed motives extend to a functor on smooth simplicial schemes over $k$. See Levine in K-theory handbook, page 475.

Consequences of representability

Yagunov on rigidity for theories represented by T-spectra. This seems to be generalized here

nLab page on Representability in algebraic geometry