4 papers
A non-spatial frame of smashing ideals
Tobias Barthel, Drew Heard
We construct commutative rings whose derived categories have non-spatial frames of smashing ideals, thereby answering in the negative questions of Balchin--Stevenson and Aoki.
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…
On the universality of multiexcisive functors
Tobias Barthel, Kaif Hilman, Nikolay Konovalov
We provide a multiplicative classification of polynomial endofunctors on spectra in terms of their Mackey functors of cross--effects. More precisely, we prove that various categori…
Homological stratification and descent
Tobias Barthel, Drew Heard, Beren Sanders +1
We introduce a notion of stratification for rigidly-compactly generated tensor-triangulated categories relative to the homological spectrum and develop the fundamental features of…