Related papers: Stratification and $\pi$-cosupport: Finite groups
A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the $\mathfrak{p}$-local…
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…
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…
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…
We develop a theory of cosupport and costratification in tensor triangular geometry. We study the geometric relationship between support and cosupport, provide a conceptual foundation for cosupport as categorically dual to support, and…
We introduce a new topological invariant of a rigidly-compactly generated tensor-triangulated category and two new notions of support. The first is based on smashing subcategories: it is unknown whether the frame of smashing subcategories…
We generalize the notion of ends and coends in category theory to the realm of module categories over finite tensor categories. We call this new concept "module (co)end". This tool allows us to give different proofs to several known results…
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…
We show that the classifying space of a $p$-local compact group is approximated by a telescope of classifying spaces of $p$-local finite groups. This result has numerous implications, like a Stable Elements Theorem for $p$-local compact…
We give necessary and sufficient conditions for stratification and costratification to descend along a coproduct preserving, tensor-exact $R$-linear functor between $R$-linear tensor-triangulated categories which are rigidly-compactly…
We develop a support theory for elementary supergroup schemes, over a field of positive characteristic $p\ge 3$, starting with a definition of a $\pi$-point generalising cyclic shifted subgroups of Carlson for elementary abelian groups and…
We present the proof assistant homotopy.io for working with finitely-presented semistrict higher categories. The tool runs in the browser with a point-and-click interface, allowing direct manipulation of proof objects via a graphical…
One of the major advantages of $\infty$-category theory over classical $1$-category theory is its robust and homotopically meaningful framework for taking (co)limits of diagrams of $\infty$-categories. However, it is both subtle and crucial…
We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…
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 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 stable module category of a finite group is canonically…
We investigate support schemes for infinitesimal unipotent supergroups and their representations. Our main results provide a non-cohomological description of these schemes which generalizes the classical work of Suslin, Friedlander, and…
We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…
The purpose of this note is to start the systematic analysis of cofinal types of topological groups.
The goal of the article is to get a satisfactory theory of cosupport in the derived category $\mathrm{D}(R)$, this is done by introducing another versions of the "big" and "small" cosupport for complexes. We provide some properties for…