Equivariant aspects of topological Hochschild homology

We study two invariants of topological Hochschild homology coming from equivariant homotopy theory: its RO(C [subscript p superscript n])-graded homotopy Mackey functors, and the regular slice filtration. In the case of RO(C [subscript p superscript n])-graded homotopy, we explain how to relate Angeltveit-Gerhardt's work to the gold elements, and in cases of interest give canonical identifications of the relevant groups in terms of the kernels of the Fontaine maps θ̃ [subscript r]. This is then used as input for studying the slice filtration on THH. When R is a torsionfree perfectoid ring, we show that the C [subscript p] -regular slice spectral sequence of THH(R; Z [subscript p]) collapses at E².