Brown representability in $\A^1$-homotopy theory
We prove the following result of V. Voevodsky. If $S$ is a finite dimensional noetherian scheme such that $S=\cup_α\Spec(R_α)$ for {\em countable} rings $R_α$, then the stable motivic homotopy category over $S$ satisfies Brown representability.
math.AG↗