67 citations · 155 across the 19 of their papers we have counts for
7 papers · 1 filter
Local Bousfield classes via homological support
Tobias Barthel, Natalia Castellana, Drew Heard +2
Given an object in a big tensor-triangulated category, we study the homological and cohomological Bousfield classes of the associated localization: the tensor-triangulated cate…
The tensor triangular geometry of fully faithful functors
Beren Sanders
We prove that the map on Balmer spectra induced by a fully faithful geometric functor is a quotient map whose fibers are connected. This is an analogue of the Zariski Connectedness…
The spectrum of excisive functors
Gregory Arone, Tobias Barthel, Drew Heard +1
We prove a thick subcategory theorem for the category of -excisive functors from finite spectra to spectra. This generalizes the Hopkins-Smith thick subcategory theorem (the $d=…
Stratification and the comparison between homological and tensor triangular support
Tobias Barthel, Drew Heard, Beren Sanders
We compare the homological support and tensor triangular support for `big' objects in a rigidly-compactly generated tensor triangulated category. We prove that the comparison map f…
Stratification in tensor triangular geometry with applications to spectral Mackey functors
Tobias Barthel, Drew Heard, Beren Sanders
We systematically develop a theory of stratification in the context of tensor triangular geometry and apply it to classify the localizing tensor-ideals of certain categories of spe…
The spectrum of derived Mackey functors
Irakli Patchkoria, Beren Sanders, Christian Wimmer
We compute the spectrum of the category of derived Mackey functors (in the sense of Kaledin) for all finite groups. We find that this space captures precisely the top and bottom la…
The spectrum of the equivariant stable homotopy category of a finite group
Paul Balmer, Beren Sanders
We study the spectrum of prime ideals in the tensor-triangulated category of compact equivariant spectra over a finite group. We completely describe this spectrum as a set for all…