Related papers: Torsion pairs via cosilting mutation

First, we show that a compact object $C$ in a triangulated category, which satisfies suitable conditions, induces a $t$-structure. Second, in an abelian category we show that a complex $P^{\centerdot}$ of small projective objects of term…

We show the existence of tilting objects in the singularity category $\mathsf{D}_{\mathsf{ Sg}}^{\mathsf{ gr}}(eAe)$ associated to certain noetherian AS-regular algebras $A$ and idempotents $e$. This gives a triangle equivalence between…

We construct tilting modules over Jacobian algebras arising from knots. To a two-bridge knot $L[a_1,\ldots,a_n]$, we associate a quiver $Q$ with potential and its Jacobian algebra $A$. We construct a family of canonical indecomposable…

Two rings A and B are said to be derived Morita equivalent if their derived categories of modules are equivalent. By results of Rickard, if A and B are derived Morita equivalent algebras over a field k, then there is a complex of bimodules…

In this work, we revisit Auslander-Buchweitz Approximation Theory and find some relations with cotorsion pairs and model category structures. From the notions of relatives generators and cogenerators in Approximation Theory, we introduce…

We present the concept of cotorsion pairs cut along subcategories of an abelian category. This provides a generalization of complete cotorsion pairs, and represents a general framework to find approximations restricted to certain…

We construct a family of $2$-tilting bundles on a Geigle-Lenzing projective space of type $(2,2,p,q)$ via the action of iterated $2$-APR mutations. As an application, we give some non-examples for an open question raised by Herschend,…

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.

We begin a study of torsion theories for representations of an important class of associative algebras over a field which includes all finite W-algebras of type A, in particular the universal enveloping algebra of gl(n) (or sl(n)) for all…

This paper classifies t-structures on the local derived category of a 3-fold flopping contraction, that are intermediate with respect to the heart of perverse coherent sheaves. Equivalently, this describes the complete lattice of torsion…

For any commutative ring $A$ we introduce a generalization of $S$--artinian rings using a hereditary torsion theory $\sigma$ instead of a multiplicative closed subset $S\subseteq{A}$. It is proved that if $A$ is a totally $\sigma$--artinian…

For a recollement $(\mathcal{A},\mathcal{B},\mathcal{C})$ of abelian categories, we show that torsion pairs in $\mathcal{A}$ and $\mathcal{C}$ can induce torsion pairs in $\mathcal{B}$; and the converse holds true under certain conditions.

The aim of this paper is to introduce tau-tilting theory, which completes (classical) tilting theory from the viewpoint of mutation. It is well-known in tilting theory that an almost complete tilting module for any finite dimensional…

Let $R$ be a ring. In this paper, we study the characterization of cosilting modules and establish a relation between cosilting modules and cotilting objects in a Grothendieck category. We proved that each cosilting right $R$-module $T$ can…

We describe in this note a torsor structure arising on the affine scheme defined by a system of rationnal algebraic relations between polyzetas at roots of unity (values of hyperlogarithmic functions on a fixed finite group of complex roots…

We study certain toric Gorenstein varieties with isolated singularities which are the quotient spaces of generic unimodular representations by the one-dimensional torus, or by the product of the one-dimensional torus with a finite abelian…

We give a complete classification of (co)torsion pairs in finite $2$-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting. These finite $2$-Calabi-Yau triangulated categories are divided into two main…

Affine Toda field theories in two dimensions constitute families of integrable, relativistically invariant field theories in correspondence with the affine Kac-Moody algebras. The particles which are the quantum excitations of the fields…

Let $S_g$ be a closed, oriented surface of genus $g$, and let $\operatorname{Mod}(S_g)$ denote its mapping class group. The Torelli group $\mathcal{I}_g$ is the subgroup of $\operatorname{Mod}(S_g)$ consisting of mapping classes that act…

We introduce the notion of joint torsion for several commuting operators satisfying a Fredholm condition. This new secondary invariant takes values in the group of invertibles of a field. It is constructed by comparing determinants…