Modulo $\tau^{p-1}$ motivic Hochschild homology of modulo $p$ motivic cohomology

Abstract

We use the motivic Greenlees spectral sequence from arXiv:2408.00338 to compute Hochschild homology in the stable motivic homotopy category over an algebraically closed field. Our target is $MHH(M\mathbb{Z}/p)/\tau^{p-1}$, where $M\mathbb{Z}/p$ is modulo $p$ motivic cohomology, $p$ a prime number different from the characteristic of the base.