A May-type spectral sequence for higher topological Hochschild homology

Abstract

Given a filtration of a commutative monoid $A$ in a symmetric monoidal stable model category $\mathcal{C}$, 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 $E_{\infty }$-ring spectra $A$ such that ${\pi }_{\ast }(A)\cong R$.

55 pages. V3. Accepted for publication in AGT. Final mock-up version including minor edits

References in corpus (2)

• Multiplicative structures on homotopy spectral sequences II
• Derived Algebraic Geometry IV: Deformation Theory

Cited by in corpus (5)

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• Whitehead Filtrations for Computations in Topological Hochschild Homology
• Maps of simplicial spectra whose realizations are cofibrations