On surjectivity in tensor triangular geometry
We prove that a jointly conservative family of geometric functors between rigidly-compactly
generated tensor triangulated categories induces a surjective map on spectra. From this we …
generated tensor triangulated categories induces a surjective map on spectra. From this we …
Descent in tensor triangular geometry
T Barthel, N Castellana, D Heard, N Naumann… - arXiv preprint arXiv …, 2023 - arxiv.org
We investigate to what extent we can descend the classification of localizing, smashing and
thick ideals in a presentably symmetric monoidal stable $\infty $-category $\mathscr {C} …
thick ideals in a presentably symmetric monoidal stable $\infty $-category $\mathscr {C} …
Lattices over finite group schemes and stratification
T Barthel, D Benson, SB Iyengar, H Krause… - arXiv preprint arXiv …, 2023 - arxiv.org
This work concerns representations of a finite flat group scheme $ G $, defined over a
noetherian commutative ring $ R $. The focus is on lattices, namely, finitely generated $ G …
noetherian commutative ring $ R $. The focus is on lattices, namely, finitely generated $ G …
Costratification and actions of tensor-triangulated categories
C Verasdanis - arXiv preprint arXiv:2211.04139, 2022 - arxiv.org
We develop the theory of costratification in the setting of relative tensor-triangular geometry,
in the sense of Stevenson, providing a unified approach to classification results of Neeman …
in the sense of Stevenson, providing a unified approach to classification results of Neeman …
Profinite equivariant spectra and their tensor-triangular geometry
S Balchin, D Barnes, T Barthel - arXiv preprint arXiv:2401.01878, 2024 - arxiv.org
We study the tensor-triangular geometry of the category of equivariant $ G $-spectra for $ G
$ a profinite group, $\mathsf {Sp} _G $. Our starting point is the construction of …
$ a profinite group, $\mathsf {Sp} _G $. Our starting point is the construction of …
The spectrum of excisive functors
We prove a thick subcategory theorem for the category of $ d $-excisive functors from finite
spectra to spectra. This generalizes the Hopkins-Smith thick subcategory theorem (the $ d …
spectra to spectra. This generalizes the Hopkins-Smith thick subcategory theorem (the $ d …
Support theories for non-Noetherian tensor triangulated categories
C Zou - arXiv preprint arXiv:2312.08596, 2023 - arxiv.org
We extend the support theory of Benson--Iyengar--Krause to the non-Noetherian setting by
introducing a new notion of small support for modules. This enables us to prove that the …
introducing a new notion of small support for modules. This enables us to prove that the …
Colocalizing subcategories of singularity categories
C Verasdanis - arXiv preprint arXiv:2311.02645, 2023 - arxiv.org
Utilizing previously established results concerning costratification in relative tensor-
triangular geometry, we classify the colocalizing subcategories of the singularity category of …
triangular geometry, we classify the colocalizing subcategories of the singularity category of …
The local-to-global principle via topological properties of the Balmer-Favi support
N Bellumat - arXiv preprint arXiv:2404.08422, 2024 - arxiv.org
Following the theory of stratification of tensor triangulated categories via Balmer-Favi
support inaugurated by Barthel, Heard and Sanders, we prove the local versions of the well …
support inaugurated by Barthel, Heard and Sanders, we prove the local versions of the well …
Colocalizing subcategories on schemes
L Alonso, A Jeremías, E Loureiro - arXiv preprint arXiv:2405.10383, 2024 - arxiv.org
A full triangulated subcategory $\mathsf {C}\subset\mathsf {T} $ of triangulated category
$\mathsf {T} $ is colocalizing if it is stable for products. If, further, $\mathsf {T} $ is monoidal …
$\mathsf {T} $ is colocalizing if it is stable for products. If, further, $\mathsf {T} $ is monoidal …