# Is There a Mayer-Vietoris Spectral Sequence of Motivic Cohomology for Closed Coverings?

For etale cohomology, there is a spectral sequence of the following form ("Mayer-Vietories spectral sequence for closed covers"):

$E_{1}^{p,q}=\oplus_{i_{0}< \cdots < i_{p}} H_{ Y_{i_{0} \cdots i_{p} }}^{q} (X, F) \Longrightarrow H_{Y}^{q-p}(X, F).$

Here, $X$ is a scheme, $Y\to X$ is a closed subscheme, and $Y_{i}$'s are a closed covering of $Y$.

$Y_{i_{0} \cdots i_{p}}$ denotes $Y_{i_{0}} \cap \cdots \cap Y_{i_{p}}.$

$F$ is an etale sheaf on $X$, and $H_{Z}^{\ast}$ denotes the cohomology with supports in a closed subscheme $Z$ on $X$.

My questions are: is there any spectral sequence of the similar form for motivic cohomology (or higher Chow group)?

If yes, then how one can prove it?

If no, then why is it?