6 papers
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…
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=…
The Balmer spectrum of pseudo-coherent complexes over a discrete valuation ring
Beren Sanders, Yufei Zhang
We study the derived category of pseudo-coherent complexes over a noetherian commutative ring, building on prior work by Matsui-Takahashi. Our main theorem is a computation of the…
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 Tate Intermediate Value Theorem
Paul Balmer, Beren Sanders
We explain how the gluing of a closed piece of the tensor-triangular spectrum with its open complement hinges on the support of the Tate ring.
Perfect complexes and completion
Paul Balmer, Beren Sanders
Let be the -adic completion of a commutative ring with respect to a finitely generated ideal . We give a necessary and sufficient criterion for the category of…