Given a filtration of a commutative monoid in a symmetric monoidal stable model category , we construct a spectral sequence analogous to the May spectral sequence whose input is the higher order topological Hochschild homology of the associated graded commutative monoid of , and whose output is the higher order topological Hochschild homology of . We then construct examples of such filtrations and derive some consequences: for example, given a connective commutative graded ring , we get an upper bound on the size of the –groups of –ring spectra such that .
"A May-type spectral sequence for higher topological Hochschild homology." Algebr. Geom. Topol. 18 (5) 2593 - 2660, 2018. https://doi.org/10.2140/agt.2018.18.2593