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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.
Federico Ernesto Mocchetti (Thu,) studied this question.