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  1. ; ; (, Bulletin of the London Mathematical Society)
    Abstract In equivariant algebra, Mackey functors play the role of abelian groups and Green and Tambara functors play the role of commutative rings. In this paper, we compute Mackey functor‐valued Tor over certain free Green and Tambara functors, generalizing the computation of Tor over a polynomial ring on one generator. In contrast with the classical situation where the resulting Tor groups vanish above degree one, we present examples where Tor is nonvanishing in almost every degree. 
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    Free, publicly-accessible full text available October 1, 2026
  2. ; (, Journal of Topology)
    Abstract We introduce and study a genuine equivariant refinement of the Tate construction associated to an extension of a finite group by a compact Lie group , which we call the parameterized Tate construction . Our main theorem establishes the coincidence of three conceptually distinct approaches to its construction when is also finite: one via recollement theory for the ‐free ‐family, another via parameterized ambidexterity for ‐local systems, and the last via parameterized assembly maps. We also show that uniquely admits the structure of a lax ‐symmetric monoidal functor, thereby refining a theorem of Nikolaus and Scholze. Along the way, we apply a theorem of the second author to reprove a result of Ayala–Mazel‐Gee–Rozenblyum on reconstructing a genuine ‐spectrum from its geometric fixed points; our method of proof further yields a formula for the geometric fixed points of an ‐complete ‐spectrum for any ‐family . 
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  3. ; ; (, Geometry & Topology)
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