Given a filtration of a commutative monoid A in a symmetric monoidal stable model category C, 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 A, and whose output is the higher order topological Hochschild homology of A. We then construct examples of such filtrations and derive some consequences: for example, given a connective commutative graded ring R, we get an upper bound on the size of the THH-groups of E 8 -ring spectra A such that π˚pAq -R. 55P42; 55T05

We compute mod (p,v1) topological Hochschild homology of the connective cover of the K(1)‐local sphere spectrum for all primes p⩾3. This is accomplished using a May‐type spectral sequence in topological Hochschild homology constructed from a filtration of a commutative ring spectrum.

In [27], Ravenel introduced sequences of spectra X(n) and T (n) which played an important role in the proof of the Nilpotence Theorem of Devinatz-Hopkins-Smith [11]. In the present paper, we solve the homotopy limit problem for topological Hochschild homology of X(n), which is a generalized version of the Segal Conjecture for the cyclic group of prime order. We prove the same theorem for T (n) under the assumption that T (n) is an E 2 -ring spectrum. This is also a first step towards computing algebraic K-theory of X(n) and T (n) using trace methods.