67 citations · 155 across the 19 of their papers we have counts for
10 papers · 1 filter
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…
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…
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 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…
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…