Related papers: On torsion torsionfree triples

In recent work, for a triangulated category $\cT$, the author introduced a topological space $\tSpec(\cT)$ which we call the triangular spectrum of $\cT$ as a tensor-free analog of the Balmer spectrum for a tensor triangulated category. In…

We prove that the dg category of perfect complexes on a smooth, proper Deligne-Mumford stack over a field of characteristic zero is geometric in the sense of Orlov, and in particular smooth and proper. On the level of triangulated…

We relate the torsion part of the Abel-Jacobi kernel in the Griffiths group of 1-cycles to a birational invariant analogous to the degree 4 unramified cohomology and an invariant associated to the generalized Hodge conjecture in degree…

The aim of this paper is to unify classification theories of torsion classes of finite dimensional algebras and commutative Noetherian rings. For a commutative Noetherian ring $R$ and a module-finite $R$-algebra $\Lambda$, we study the set…

Let $k$ be an algebraically closed field of characteristic $p\ge 0$. Let $G$ be an affine group scheme over $k$. We classify the indecomposable exact module categories over the rigid tensor category $\text{Coh}_f(G)$ of coherent sheaves of…

This paper provides a systematic treatment of Gorenstein homological aspects for cleft extensions of rings. In particular, we investigate Goresnteinness, Gorenstein projective modules and singularity categories in the context of cleft…

There is a conjecture, that the torsionfreeness of the module of differentials in a point of an algebraic or algebroid curve should imply that the curve is non singular at that point. A report on the main results is given.

Consider three normalised cuspidal eigenforms of weight $2$ and prime level $p$. Under the assumption that the global root number of the associated triple product $L$-function is $+1$, we prove that the complex Abel-Jacobi image of the…

We obtain a presentation of the t-deformed Grothendieck ring of a quantum loop algebra of Dynkin type A, D, E. Specializing t at the the square root of the cardinality of a finite field F, we obtain an isomorphism with the derived Hall…

We study the algebraic structure of the automorphism group of the derived category of coherent sheaves on a smooth projective variety twisted by a Brauer class. Our main results generalize results of Rouquier in the untwisted case.

We establish a correspondence between recollements of abelian categories up to equivalence and certain TTF-triples. For a module category we show, moreover, a correspondence with idempotent ideals, recovering a theorem of Jans. Furthermore,…

Let $X$ be a normal algebraic variety over an algebraically closed field $k$ of characteristic zero. We prove that the K\"{a}hler differential sheaf of $X$ is torsion-free if and only if any regular section of the ideal sheaf of the first…

For a commutative, unital and integral quantale V, we generalize to V-groups the results developed by Gran and Michel for preordered groups. We first of all show that, in the category V-Grp of V-groups, there exists a torsion theory whose…

We apply the technique of recollement to study the Gorenstein defect categories of triangular matrix algebras. First, we construct a left recollement of Gorenstein defect categories for a triangular matrix algebra under some conditions,…

We show that the derived category of any singularity over a field of characteristic 0 can be embedded fully and faithfully into a smooth triangulated category which has a semiorthogonal decomposition with components equivalent to derived…

Curved A-infinity algebras appear in nature as deformations of dg algebras. We develop the basic theory of curved A-infinity algebras and, in particular, curved dg algebras. We investigate their link with a suitable class of dg coalgebras…

Let $\operatorname{TFAb}_r$ be the class of torsion-free abelian groups of rank $r$, and let $\operatorname{FD}_r$ be the class of fields of characteristic $0$ and transcendence degree~$r$. We compare these classes using various notions.…

This paper studies the basic K-theoretic properties of a triangulated persistence category (TPC). This notion was introduced in our earlier papers on triangulation, persistence, and Fukaya categories (arXiv:2304.01785 and arXiv:2104.12258)…

Given a torsion pair $\mathbf{t} = (\mathcal{T} ;\mathcal{F})$ in a module category $R$-Mod we give necessary and sufficient conditions for the associated Happel-Reiten-Smal\o $\text{ }$ t-structure in $\mathcal{D}(R)$ to have a heart…

The main aim of this paper is to study chains of model structures arising from cotorsion pairs in extriangulated categories. Starting with a hereditary Hovey triple, we construct further hereditary Hovey triples whose homotopy categories…