67 citations · 155 across the 19 of their papers we have counts for
21 papers
The Serre-Grothendieck Finiteness Theorem for the cohomology of coherent sheaves
Beren Sanders
We prove the converse of the Serre-Grothendieck finiteness theorem for the cohomology of coherent sheaves, originally due to Lipman. This result characterizes proper morphisms as t…
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 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.
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…
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…
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=…
Descent in tensor triangular geometry
Tobias Barthel, Natalia Castellana, Drew Heard +3
We investigate to what extent we can descend the classification of localizing, smashing and thick ideals in a presentably symmetric monoidal stable -category …
On surjectivity in tensor triangular geometry
Tobias Barthel, Natalia Castellana, Drew Heard +1
We prove that a jointly conservative family of geometric functors between rigidly-compactly generated tensor triangulated categories induces a surjective map on Balmer spectra. Fro…
Cosupport in tensor triangular geometry
Tobias Barthel, Natalia Castellana, Drew Heard +1
We develop a theory of cosupport and costratification in tensor triangular geometry. We study the geometric relationship between support and cosupport, provide a conceptual foundat…
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…
A characterization of finite étale morphisms in tensor triangular geometry
Beren Sanders
We provide a characterization of finite étale morphisms in tensor triangular geometry. They are precisely those functors which have a conservative right adjoint, satisfy Grothendie…
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 compactness locus of a geometric functor and the formal construction of the Adams isomorphism
Beren Sanders
We introduce the compactness locus of a geometric functor between rigidly-compactly generated tensor-triangulated categories, and describe it for several examples arising in equiva…
A note on triangulated monads and categories of module spectra
Ivo Dell'Ambrogio, Beren Sanders
Consider a monad on an idempotent complete triangulated category with the property that its Eilenberg-Moore category of modules inherits a triangulation. We show that any other tri…
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…
Grothendieck-Neeman duality and the Wirthmüller isomorphism
Paul Balmer, Ivo Dell'Ambrogio, Beren Sanders
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 existen…
Restriction to finite-index subgroups as étale extensions in topology, KK-theory and geometry
Paul Balmer, Ivo Dell'Ambrogio, Beren Sanders
For equivariant stable homotopy theory, equivariant KK-theory and equivariant derived categories, we show how restriction to a subgroup of finite index yields a finite commutative…
Higher comparison maps for the spectrum of a tensor triangulated category
Beren Sanders
For each object in a tensor triangulated category, we construct a natural continuous map from the object's support---a closed subset of the category's triangular spectrum---to the…