Related papers: Re-framing the classification of ideals in noncomm…

In this paper, we study geometric points in tensor triangular geometry. In doing so, we construct a counter-example to Balmer's Nerves of Steel conjecture using free constructions in higher Zariski geometry. We then go on to introduce and…

We prove that a jointly conservative family of geometric functors between rigidly-compactly generated tensor triangulated categories induces a surjective map on Balmer spectra. From this we deduce a fiberwise criterion for Balmer's…

We consider a Deligne-Mumford stack $X$ which is the quotient of an affine scheme $\operatorname{Spec}A$ by the action of a finite group $G$ and show that the Balmer spectrum of the tensor triangulated category of perfect complexes on $X$…

We use minimal tilting complexes to construct an explicit bijection between the set of thick tensor ideals with the two-out-of-three property in the category of finite-dimensional modules over a quantum group at a root of unity and the set…

Let $X$ be a quasi-compact algebraic stack with quasi-finite and separated diagonal. We classify the thick $\otimes$-ideals of $\mathsf{D}_{\mathrm{qc}}(X)^c$. If $X$ is tame, then we also compute the Balmer spectrum of the…

We study operator algebras arising from monomial ideals in the ring of polynomials in noncommuting variables, through the apparatus of subproduct systems and C*-correspondences. We provide a full comparison amongst the related operator…

We introduce a new type of categorical object called a \emph{hom-tensor category} and show that it provides the appropriate setting for modules over an arbitrary hom-bialgebra. Next we introduce the notion of \emph{hom-braided category} and…

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 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 context, we investigate connections between big prime…

Given a support variety theory defined on the compact part of a monoidal triangulated category, we define an extension to the non-compact part following the blueprint of Benson--Carlson--Rickard, Benson--Iyengar--Krause, Balmer--Favi, and…

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 subsets detect tt-ideals and we prove that any infinite…

We study the Balmer spectrum of the category of finite G-spectra for a compact Lie group G, extending the work for finite G by Strickland, Balmer-Sanders, Barthel-Hausmann-Naumann-Nikolaus-Noel-Stapleton and others. We give a description of…

Given a tensor-triangulated category $T$, we prove that every flat tensor-idempotent in the module category over $T^c$ (the compacts) comes from a unique smashing ideal in $T$. We deduce that the lattice of smashing ideals forms a frame.

We introduce a notion of stratification for rigidly-compactly generated tensor-triangulated categories relative to the homological spectrum and develop the fundamental features of this theory. In particular, we demonstrate that it exhibits…

We extend work of Balmer, associating filtrations of essentially small tensor triangulated categories to certain dimension functions, to the setting of actions of rigidly-compactly generated tensor triangulated categories on compactly…

We describe a general framework for prime, completely prime, semiprime, and primitive ideals of an abelian 2-category. This provides a noncommutative version of Balmer's prime spectrum of a tensor triangulated category. These notions are…

Let F be a field of characteristic different than 2. We establish surjectivity of Balmer's comparison map rho^* from the tensor triangular spectrum of the homotopy category of compact motivic spectra to the homogeneous Zariski spectrum of…

We study the composition of Bousfield localizations on a tensor triangulated category stratified via the Balmer-Favi support and with noetherian Balmer spectrum. Our aim is to provide reductions via purely axiomatic arguments, allowing us…

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 prove that the map on Balmer spectra induced by a fully faithful geometric functor is a quotient map whose fibers are connected. This is an analogue of the Zariski Connectedness Theorem in algebraic geometry and it can be applied to a…