A motivic Greenlees spectral sequence towards motivic Hochschild homology

TL;DR

This paper introduces a motivic Greenlees spectral sequence to compute motivic Hochschild homology, providing new tools for understanding the homotopy rings of motivic spectra over algebraically closed fields.

Contribution

It defines a motivic Greenlees spectral sequence and applies it to compute the homotopy ring of a motivic spectrum related to topological Hochschild homology over algebraically closed fields.

Findings

Spectral sequence converges to motivic Hochschild homology.

Homotopy ring of the spectrum is determined in specific cases.

Provides a new computational approach in motivic homotopy theory.

Abstract

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 $p$.