Cosupport in tensor triangular geometry
We develop a theory of cosupport and costratification in tensor triangular geometry. We
study the geometric relationship between support and cosupport, provide a conceptual …
study the geometric relationship between support and cosupport, provide a conceptual …
Quillen stratification in equivariant homotopy theory
T Barthel, N Castellana, D Heard, N Naumann… - arXiv preprint arXiv …, 2023 - arxiv.org
We prove a version of Quillen's stratification theorem in equivariant homotopy theory for a
finite group $ G $, generalizing the classical theorem in two directions. Firstly, we work with …
finite group $ G $, generalizing the classical theorem in two directions. Firstly, we work with …
Stratification and the comparison between homological and tensor triangular support
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 …
rigidly-compactly generated tensor triangulated category. We prove that the comparison …
[PDF][PDF] A characterization of finite\'etale morphisms in tensor triangular geometry
B Sanders - Épijournal de Géométrie Algébrique, 2022 - epiga.episciences.org
We provide a characterization of nite étale morphisms in tensor triangular geometry. They
are precisely those functors which have a conservative right adjoint, satisfy Grothendieck …
are precisely those functors which have a conservative right adjoint, satisfy Grothendieck …
Stratifying integral representations of finite groups
T Barthel - arXiv preprint arXiv:2109.08135, 2021 - arxiv.org
We classify the localizing tensor ideals of the integral stable module category for any finite
group $ G $. This results in a generic classification of $\mathbb {Z}[G] $-lattices of finite and …
group $ G $. This results in a generic classification of $\mathbb {Z}[G] $-lattices of finite and …
Prismatic decompositions and rational -spectra
S Balchin, T Barthel, JPC Greenlees - arXiv preprint arXiv:2311.18808, 2023 - arxiv.org
We study the tensor-triangular geometry of the category of rational $ G $-spectra for a
compact Lie group $ G $. In particular, we prove that this category can be naturally …
compact Lie group $ G $. In particular, we prove that this category can be naturally …
Duality pairs, phantom maps, and definability in triangulated categories
I Bird, J Williamson - arXiv preprint arXiv:2202.08113, 2022 - arxiv.org
We define duality triples and duality pairs in compactly generated triangulated categories
and investigate their properties. This enables us to give an elementary way to determine …
and investigate their properties. This enables us to give an elementary way to determine …
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 …
The homological spectrum via definable subcategories
I Bird, J Williamson - arXiv preprint arXiv:2304.05179, 2023 - arxiv.org
We develop an alternative approach to the homological spectrum through the lens of
definable subcategories. This culminates in a proof that the homological spectrum is …
definable subcategories. This culminates in a proof that the homological spectrum is …
Stratification and the smashing spectrum
C Verasdanis - Mathematische Zeitschrift, 2023 - Springer
We develop the theory of stratification for a rigidly-compactly generated tensor-triangulated
category using the smashing spectrum and the small smashing support. Within the stratified …
category using the smashing spectrum and the small smashing support. Within the stratified …