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Related papers: Universal localisations via silting

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We classify all tilting and cotilting classes over commutative noetherian rings in terms of descending sequences of specialization closed subsets of the Zariski spectrum. Consequently, all resolving subcategories of finitely generated…

Commutative Algebra · Mathematics 2014-06-03 Lidia Angeleri Hügel , David Pospisil , Jan Stovicek , Jan Trlifaj

Recent results by Keller and Nicol{\'a}s and by Koenig and Yang have shown bijective correspondences between suitable classes of t-structures and co-t-structures with certain objects of the derived category: silting objects. On the other…

Representation Theory · Mathematics 2013-11-12 Qunhua Liu , Jorge Vitoria , Dong Yang

In this paper, we consider the endomorphism algebras of infinitely generated tilting modules of the form $R_{\mathcal U}\oplus R_{\mathcal U}/R$ over tame hereditary $k$-algebras $R$ with $k$ an arbitrary field, where $R_{\mathcal{U}}$ is…

Representation Theory · Mathematics 2015-03-18 Hongxing Chen , Changchang Xi

We consider recollements of derived categories of dg-algebras induced by self orthogonal compact objects obtaining a generalization of Rickard's Theorem. Specializing to the case of partial tilting modules over a ring, we extend the results…

Rings and Algebras · Mathematics 2013-01-08 Silvana Bazzoni , Alice Pavarin

We study smashing subcategories of a triangulated category with coproducts via silting theory. Our main result states that for derived categories of dg modules over a non-positive differential graded ring, every compactly generated…

Representation Theory · Mathematics 2019-02-18 Lidia Angeleri Hügel , Frederik Marks , Jorge Vitória

We introduce Gorenstein silting modules (resp. complexes), and give the relation with the usual silting modules (resp. complexes). We show that Gorenstein silting modules are the module-theoretic counterpart of 2-term Gorenstein silting…

Commutative Algebra · Mathematics 2021-12-30 Nan Gao , Jing Ma , Chiheng Zhang

We classify all tilting classes over an arbitrary commutative ring via certain sequences of Thomason subsets of the spectrum, generalizing the classification for noetherian commutative rings by…

Commutative Algebra · Mathematics 2020-03-24 Michal Hrbek , Jan Šťovíček

In this paper, we investigate a non-commutative version of strongly flat modules, which is based on the concept of universal localization introduced by Cohn. We consider a set $\sigma$ consisting of maps of finitely generated projective…

Representation Theory · Mathematics 2025-08-11 Javad Asadollahi , Rasool Hafezi , Somayeh Sadeghi

The notion of cosilting module was recently introduced as a generalization of the notion of cotilting module. In this paper, we give a characterization of (partial) cosilting modules in terms of two-term cosilting complexes. Moreover, we…

Representation Theory · Mathematics 2016-11-23 Flaviu Pop

If R is a triangular 2x2 matrix ring, the columns, P and Q, are projective left R-modules. We describe the universal localization of R which makes invertible an R-module morphism P --> Q, generalizing a theorem of A.Schofield. We also…

Rings and Algebras · Mathematics 2007-05-23 Desmond Sheiham

Given a diagram of rings, one may consider the category of modules over them. We are interested in the homotopy theory of categories of this type: given a suitable diagram of model categories M(s) (as s runs through the diagram), we…

Algebraic Topology · Mathematics 2013-09-27 J. P. C. Greenlees , B. Shipley

Mutation of compact silting objects is a fundamental operation in the representation theory of finite-dimensional algebras due to its connections to cluster theory and to the lattice of torsion pairs in module or derived categories. In this…

Representation Theory · Mathematics 2025-06-18 Lidia Angeleri Hügel , Rosanna Laking , Jan Šťovíček , Jorge Vitória

We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in any triangulated category D with arbitrary (set-indexed) coproducts. We show that equivalence classes of partial silting sets are in bijection…

Representation Theory · Mathematics 2018-07-05 Pedro Nicolas , Manuel Saorin , Alexandra Zvonareva

A classic result by Raynaud and Gruson says that the notion of an (infinite dimensional) vector bundle is Zariski local. This result may be viewed as a particular instance (for n = 0) of the locality of more general notions of…

Representation Theory · Mathematics 2021-09-10 Michal Hrbek , Jan Šťovíček , Jan Trlifaj

Let $R$ be a commutative Noetherian ring with non-zero identity, $\fa$ an ideal of $R$, $M$ a finite $R$--module and $X$ an arbitrary $R$--module. Here, we show that, in the Serre subcategories of the category of $R$--modules, how the…

Commutative Algebra · Mathematics 2013-09-12 Alireza Vahidi , Moharram Aghapournahr

Extriangulated categories give a simultaneous generalization of triangulated categories and exact categories. In this paper, we study silting subcategories of an extriangulated category. First, we show that a silting subcategory induces a…

Representation Theory · Mathematics 2023-04-11 Takahide Adachi , Mayu Tsukamoto

We study infinite dimensional tilting modules over a concealed canonical algebra of domestic or tubular type. In the domestic case, such tilting modules are constructed by using the technique of universal localization, and they can be…

Representation Theory · Mathematics 2019-11-07 Lidia Angeleri Hügel , Dirk Kussin

Given a small category C, we show that there is a universal way of expanding C into a model category, essentially by formally adjoining homotopy colimits. The technique of localization becomes a method for imposing `relations' into these…

Algebraic Topology · Mathematics 2007-05-23 Daniel Dugger

We classify the localizing tensor ideals of the integral stable module category for any finite group $G$. This results in a generic classification of $\mathbb{Z}[G]$-lattices of finite and infinite rank and globalizes the modular case…

Representation Theory · Mathematics 2021-09-17 Tobias Barthel

Recently, tilting and cotilting classes over commutative noetherian rings have been classified in arXiv:1203.0907. We proceed and, for each n-cotilting class C, construct an n-cotilting module inducing C by an iteration of injective…

Commutative Algebra · Mathematics 2014-07-08 Jan Stovicek , Jan Trlifaj , Dolors Herbera