We construct localization cofibration sequences for the topological Hochschild homology
(THH) and topological cyclic homology (TC) of small spectral categories. Using a global …

We explore the C 2–equivariant spectra Tmf 1 (3) and TMF 1 (3). In particular, we compute
their C 2–equivariant Picard groups and the C 2–equivariant Anderson dual of Tmf 1 (3) …

Let G be a finite extension of a torus. Working with highly structured ring and module
spectra, let M be any module over MU; examples include all of the standard homotopical MU …

We give a full classification of representation types of the subcategories of representations of
an m× n rectangular grid with monomorphisms (dually, epimorphisms) in one or both …

We describe a comparison between pretriangulated differential graded categories and
certain stable infinity categories. Specifically, we use a model category structure on …

This paper contains an overview of background from stable homotopy theory used by Freed–
Hopkins in their work on invertible extended topological field theories. We provide a working …

Let A→ B be a G-Galois extension of rings, or more generally of E∞-ring spectra in the
sense of Rognes. A basic question in algebraic K-theory asks how close the map K (A)→ K …

We clarify the relationship between Grothendieck duality à la Neeman and the Wirthmüller
isomorphism à la Fausk–Hu–May. We exhibit an interesting pattern of symmetry in the …

The idea for this book was conceptualized during a research visit to Macquarie University in
the summer of 2017. At first, I was interested in collecting exotic examples of model …

Homotopy limits and colimits are homotopical replacements for the usual limits and colimits
of category theory, which can be approached either using classical explicit constructions or …