Related papers: The spectrum of local dualisable modular represent…

The aim of this paper is to explain how to get a complex of smooth representations out of the dual vector space to a smooth representation of a p-adic Lie group, in natural characteristic. The construction does not depend on any…

We show that a $\mathbb{P}$-object and simple configurations of $\mathbb{P}$-objects have a formal derived endomorphism algebra. Hence the triangulated category (classically) generated by such objects is independent of the ambient…

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 study the structure of the category of graded, connected, countable-dimensional, commutative and cocommutative Hopf algebras over a perfect field $k$ of characteristic $p$. Every $p$-torsion object in this category is uniquely a direct…

We study the triangulated subcategories of compact objects in stable homotopy categories such as the homotopy category of spectra, the derived categories of rings, and the stable module categories of Hopf algebras. In the first part of this…

The representations of a quiver Q over a field k have been studied for a long time. It seems to be worthwhile to consider also representations of Q over arbitrary finite-dimensional k-algebras A. Here we draw the attention to the case when…

We introduce a general theory of parametrized objects in the setting of infinity categories. Although spaces and spectra parametrized over spaces are the most familiar examples, we establish our theory in the generality of objects of a…

In this article, gentle algebras are realised as tiling algebras, which are associated to partial triangulations of unpunctured surfaces with marked points on the boundary. This notion of tiling algebras generalise the notion of Jacobian…

This paper examines the dimension of the graded local cohomology $H_\mathfrak{m}^p(S/K^s)_\gamma$ and $H_\mathfrak{m}^p(S/K^{(s)})$ for a monomial ideal $K$. This information is encoded in the reduced homology of a simplicial complex called…

Let $G$ be a finite group, and let $\mathbf{K}_p$ denote the completion at $p$ of the complex $K$-theory spectrum. $\mathbf{K}_p$ is a commutative ring spectrum that in some ways is very similar to the usual ring $\mathbf{Z}_p$ of $p$-adic…

Using homological residue fields, we define supports for big objects in tensor-triangulated categories and prove a tensor-product formula.

Consider a topological surface $\Sigma$. We introduce the spectrum of a representation from the fundamental group of $\Sigma$ to SL(2,R), which is a subset of projective measured lamination on the surface, which captures the directions…

Borel--Serre proved that for a number ring $R$ with fraction field $K$, the symplectic group $\text{Sp}_{2n}(R)$ is a virtual duality group of degree quadratic in $n$, and that the symplectic Steinberg module $\text{St}^\omega_{2n}(K)$ is…

For the algebra $A$ in the title, its prime, primitive and maximal spectra are classified. The group of automorphisms of $A$ is determined. The simple unfaithful $A$-modules and the simple weight $A$-modules are classified.

For a finite dimensional algebra $A$, we establish correspondences between torsion classes and wide subcategories in $mod(A)$. In case $A$ is representation finite, we obtain an explicit bijection between these two classes of subcategories.…

Let $G$ be a finite group. We re-analyze the splitting of rational $G$-spectra, which is discussed in Barne's thesis and traces back to Greenlees and May. We will study how the splitting behaves under a localization which is weaker than…

We define an inner product (suitably interpreted) on the K(n)-local spectrum LG := L_{K(n)}BG_+, where G is a finite group or groupoid. This gives an inner product on E^*BG_+ for suitable K(n)-local ring spectra E. We relate this to the…

Colocalization is a right adjoint to the inclusion of a subcategory. Given a ring-spectrum R, one would like a spectral sequence which connects a given colocalization in the derived category of R-modules and an appropriate colocalization in…

We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. The category of…

Following Krause \cite{Kr}, we prove Krull-Schmidt type decomposition theorems for thick subcategories of various triangulated categories including the derived categories of rings, Noetherian stable homotopy categories, stable module…