Related papers: Thick Subcategories of Discrete Derived Categories
We classify the category of finite-dimensional real division composition algebras having a non-abelian Lie algebra of derivations. Our complete and explicit classification is largely achieved by introducing the concept of a…
We study complexes of finite complete intersection dimension in the derived category of a local ring. Given such a complex, we prove that the thick subcategory it generates contains complexes of all possible complexities. In particular, we…
Diffusion models form an important class of generative models today, accounting for much of the state of the art in cutting edge AI research. While numerous extensions beyond image and video generation exist, few of such approaches address…
In this paper we construct a tilting sheaf for Severi-Brauer Varieties and Involution Varieties. This sheaf relates the derived category of each variety to the derived category of modules over a ring whose semisimple component consists of…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…
We consider smooth algebraic varieties with ample either canonical or anticanonical sheaf. We prove that such a variety is uniquely determined by its derived category of coherent sheaves. We also calculate the group of exact…
We show that the Segal topos of derived stacks over simplicial commutative $k$-algebras, which can be used to model natural phenomena, has a subobject classifier, something we regard as being a source from which dynamics is generated. This…
We investigate for which linear-algebraic groups (over the complex numbers or any local field) there exists subgroups which are dense in the Zariski topology, but discrete in the Hausdorff topology. For instance, such subgroups exist for…
We give a block decomposition of the dg category of character sheaves on a simple and simply-connected complex reductive group $G$, similar to the one in generalized Springer correspondence. As a corollary, we identify the category of…
Recollements of triangulated categories may be seen as exact sequences of such categories. Iterated recollements of triangulated categories are analogues of geometric or topological stratifications and of composition series of algebraic…
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any…
We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with…
In this paper, we investigate properties of the bounded derived category of finite dimensional modules over a gentle or skew-gentle algebra. We show that the Rouquier dimension of the derived category of such an algebra is at most one.…
We constructed a product network based on the sales data collected and provided by a Fortune 500 speciality retailer. The structure of the network is dominated by small isolated components, dense clique-based communities, and sparse stars…
Restriction categories were established to handle maps that are partially defined with respect to composition. Tensor topology realises that monoidal categories have an intrinsic notion of space, and deals with objects and maps that are…
Various classification theorems of thick subcategories of a triangulated category have been obtained in many areas of mathematics. In this paper, as a higher-dimensional version of the classification theorem of thick subcategories of the…
We present and characterize the classes of Grothendieck toposes having enough supercompact objects or enough compact objects. In the process, we examine the subcategories of supercompact objects and compact objects within such toposes and…
We discuss derived categories of coherent sheaves on algebraic varieties. We focus on the case of non-singular Calabi-Yau varieties and consider two unsolved problems: proving that birational varieties have equivalent derived categories,…
We introduce continuous Frobenius categories. These are topological categories which are constructed using representations of the circle over a discrete valuation ring. We show that they are Krull-Schmidt with one indecomposable object for…
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…