67 citations · 453 across the 47 of their papers we have counts for
16 papers · 1 filter
Patch-density in tensor-triangular geometry
Paul Balmer, Martin Gallauer
The spectrum of a tensor-triangulated category carries a compact Hausdorff topology, called the constructible topology, also known as the patch topology. We prove that patch-dense…
Universal support for triangulated categories
Paul Balmer, Pablo S. Ocal
We revisit a result of Gratz and Stevenson on the universal space that carries supports for objects of a triangulated category, in the absence of a tensor product.
Cohomological Mackey 2-functors
Paul Balmer, Ivo Dell'Ambrogio
We show that the bicategory of finite groupoids and right-free permutation bimodules is a quotient of the bicategory of Mackey 2-motives introduced in arXiv:1808.04902, obtained by…
Computing homological residue fields in algebra and topology
Paul Balmer, James C. Cameron
We determine the homological residue fields, in the sense of tensor-triangular geometry, in a series of concrete examples ranging from topological stable homotopy theory to modular…
Relative stable categories and birationality
Paul Balmer, Greg Stevenson
We propose a general method to construct new triangulated categories, relative stable categories, as additive quotients of a given one. This construction enhances results of Beligi…
Homological support of big objects in tensor-triangulated categories
Paul Balmer
Using homological residue fields, we define supports for big objects in tensor-triangulated categories and prove a tensor-product formula.
Green equivalences in equivariant mathematics
Paul Balmer, Ivo Dell'Ambrogio
We establish Green equivalences for all Mackey 2-functors, without assuming Krull-Schmidt. By running through the examples of Mackey 2-functors, we recover all variants of the Gree…
Nilpotence theorems via homological residue fields
Paul Balmer
We prove nilpotence theorems in tensor-triangulated categories using suitable Gabriel quotients of the module category, and discuss examples.
Tensor-triangular fields: Ruminations
Paul Balmer, Henning Krause, Greg Stevenson
We examine the concept of field in tensor-triangular geometry. We gather examples and discuss possible approaches, while highlighting open problems. As the construction of residue…
On the surjectivity of the map of spectra associated to a tensor-triangulated functor
Paul Balmer
We prove a few results about the map induced on tensor-triangular spectra by a tensor-triangulated functor . First, is conservative if and only if is surje…
The frame of smashing tensor-ideals
Paul Balmer, Henning Krause, Greg Stevenson
Given a tensor-triangulated category , we prove that every flat tensor-idempotent in the module category over (the compacts) comes from a unique smashing ideal in . We…
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…
The derived category of an étale extension and the separable Neeman-Thomason theorem
Paul Balmer
We prove that etale morphisms of schemes yield separable extensions of derived categories. We then generalize the Neeman-Thomason Localization Theorem to separable extensions of tr…
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…
Separable extensions in tensor-triangular geometry and generalized Quillen stratification
Paul Balmer
We study the continuous map induced on spectra by a separable extension of tensor-triangulated categories. We determine the image of this map and relate the cardinality of its fibe…
The spectrum of prime ideals in tensor triangulated categories
Paul Balmer
We define the spectrum of a tensor triangulated category as the set of so-called prime ideals, endowed with a suitable topology. In this very generality, the spectrum is the un…