Related papers: (Co)stratification of stable categories for infini…
The tensor ideal localising subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning…
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 infinite rank and globalizes the modular case…
We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…
We introduce the notion of $\pi$-cosupport as a new tool for the stable module category of a finite group scheme. In the case of a finite group, we use this to give a new proof of the classification of tensor ideal localising subcategories.…
The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived…
We survey some methods developed in a series of papers, for classifying localising subcategories of tensor triangulated categories. We illustrate these methods by proving a new theorem, providing such a classification in the case of the…
The Hom closed colocalising subcategories of the stable module category of a finite group scheme are classified. This complements the classification of the tensor closed localising subcategories in our previous work. Both classifications…
In this work we construct a compactly generated tensor-triangulated stable category for a large class of infinite groups, including those in Kropholler's hierarchy $\mathrm{LH}\mathfrak{F}$. This can be constructed as the homotopy category…
We construct a well-behaved stable category of modules for a large class of infinite groups. We then consider its Picard group, which is the group of invertible (or endotrivial) modules. We show how this group can be calculated when the…
Given a finite cocommutative Hopf algebra $A$ over a commutative regular ring $R$, the lattice of localising tensor ideals of the stable category of Gorenstein projective $A$-modules is described in terms of the corresponding lattices for…
We state and prove a stratification result that allows us to classify the tensor ideal localizing subcategories for the stable module category $\text{Stab}(\mathcal{C}_{(\mathfrak{g}, \mathfrak{g}_{\bar 0})})$ of Lie superalgbera…
We develop a suitable version of the stable module category of a finite group G over an arbitrary commutative ring k. The purpose of the construction is to produce a compactly generated triangulated category whose compact objects are the…
One of the most useful methods for studying the stable homotopy category is localising at some spectrum E. For an arbitrary stable model category we introduce a candidate for the E-localisation of this model category. We study the…
The localising subcategories of the derived category of the cochains on the classifying space of a finite group are classified. They are in one to one correspondence with the subsets of the set of homogeneous prime ideals of the cohomology…
This work concerns the stable module category of a finite group over a field of characteristic dividing the group order. The minimal localising tensor ideals correspond to the non-maximal homogeneous prime ideals in the cohomology ring of…
We introduce the stable module $\infty$-category for groups of type $\Phi$ as an enhancement of the stable category defined by N. Mazza and P. Symonds. For groups of type $\Phi$ which act on a tree, we show that the stable module…
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 finite groups. We also make significant progress in…
This paper is an expository account of the theory of stable infinity categories. We prove that the homotopy category of a stable infinity category is triangulated, and that the collection of stable infinity categories is closed under a…
We investigate the particular properties of the stable category of modules over a finite dimensional cocommutative graded connected Hopf algebra $A$, via tensor-triangulated geometry. This study requires some mild conditions on the Hopf…
A full triangulated subcategory $\mathsf{L} \subset \mathsf{T}$ of triangulated category $\mathsf{T}$ is \emph{localizing} if it is stable for coproducts. If, further, $\mathsf{T}$ is $\otimes$-triangulated, we say that $\mathsf{L}$ is…