  We define a motivic Greenlees spectral sequence by characterising an
associated $t$-structure. We then examine a motivic version of topological
Hochschild homology for the motivic cohomology spectrum modulo a prime number
$p$. Finally, we use the motivic Greenlees spectral sequence to determine the
homotopy ring of a related spectrum, given that the base field is algebraically
closed with a characteristic that is coprime to $p$.
