Localization, Slice Tower, and Motivic Spectra

Suppose $k$ is an algebraically closed field of characteristic $p>0$. There is an $\infty$-category of motivic spectra over $k$, denoted $\mathcal{S}pt(k)$. As in algebraic topology, there are motivic Eilenberg-Maclane spectra $\mathbf{EM}(A)$ for each abelian group $A$. I have a few related questions:

1) Do $\mathbf{EM}(\mathbb{Z}[1/p])\wedge(-)$ and $\mathbf{EM}(\mathbb{Z}_{\ell})\wedge(-)$, for $\ell\neq p$ preserve cofiber sequences?

2) Do these operations commute with the formation of slices?

3) What is a good theory of inverting $p$ or completing at $\ell\neq p$ in $\mathcal{S}pt(k)$ or its homotopy category $\mathcal{SH}(k)$ that behaves well with respect to the formation of slices and cofiber sequences?

Thank you!

• (2) is false because motivic eilenberg maclane spectra have only one slice whereas the sphere has many. For (1), the derived smash product is exact in both variables, so preserves distinguished triangles (on the homotopy category). I'm not sure if this answers your question. Nov 7, 2016 at 9:38