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Stably semiorthogonally indecomposable varieties [PDF]
Épijournal de Géométrie Algébrique, 2023 A triangulated category is said to be indecomposable if it admits no nontrivial semiorthogonal decompositions. We introduce a definition of a noncommutatively stably semiorthogonally indecomposable (NSSI) variety. This propery implies, among other things,
Dmitrii Pirozhkov
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Noncommutative tensor triangulated categories and coherent frames
Comptes Rendus. Mathématique, 2023 We develop a point-free approach for constructing the Nakano–Vashaw–Yakimov–Balmer spectrum of a noncommutative tensor triangulated category under certain assumptions.
Mallick, Vivek Mohan, Ray, Samarpita
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Homotopy cartesian squares in extriangulated categories
Open Mathematics, 2023 Let (C,E,s)\left({\mathcal{C}},{\mathbb{E}},{\mathfrak{s}}) be an extriangulated category. Given a composition of two commutative squares in C{\mathcal{C}}, if two commutative squares are homotopy cartesian, then their composition is also a homotopy ...
He Jing, Xie Chenbei, Zhou Panyue
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Homological dimension based on a class of Gorenstein flat modules
Comptes Rendus. Mathématique, 2023 In this paper, we study the relative homological dimension based on the class of projectively coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and Stovicek in [26].
Dalezios, Georgios, Emmanouil, Ioannis
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Completions of discrete cluster categories of type A
Transactions of the London Mathematical Society, 2021 We complete the discrete cluster categories of type A as defined by Igusa and Todorov, by embedding such a discrete cluster category inside a larger one, and then taking a certain Verdier quotient.
Charles Paquette, Emine Yıldırım
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Teacher - an architect of children preschool education during pandemic Covid – 19 [PDF]
Studia z Teorii Wychowania, 2023 IntroductionThe scope of researches was built around one main category, that is the category of change, which occurred in preschool education during Covid-19 period.Aim of conducted researches:The main objective was to display outcomes of conducted ...
Jolanta Andrzejewska +2 more
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q-deformed rational numbers and the 2-Calabi–Yau category of type $A_{2}$
Forum of Mathematics, Sigma, 2023 We describe a family of compactifications of the space of Bridgeland stability conditions of a triangulated category, following earlier work by Bapat, Deopurkar and Licata. We particularly consider the case of the 2-Calabi–Yau category of the $A_2$
Asilata Bapat +2 more
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Homological Bondal-Orlov localization conjecture for rational singularities
Forum of Mathematics, Sigma, 2023 Given a resolution of rational singularities $\pi \colon {\tilde {X}} \to X$ over a field of characteristic zero, we use a Hodge-theoretic argument to prove that the image of the functor ${\mathbf {R}}\pi _*\colon {\mathbf {D}}^{\mathrm {b}}({\
Mirko Mauri, Evgeny Shinder
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TILTING THEORY FOR GORENSTEIN RINGS IN DIMENSION ONE
Forum of Mathematics, Sigma, 2020 In representation theory, commutative algebra and algebraic geometry, it is an important problem to understand when the triangulated category $\mathsf{D}_{\operatorname{sg}}^{\mathbb{Z}}(R)=\text{}\underline{\mathsf{CM}}_{0}^{\mathbb{Z}}R$ admits a ...
RAGNAR-OLAF BUCHWEITZ +2 more
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How to glue derived categories
Bulletin of Mathematical Sciences, 2018 We give an overview of existing enhancement techniques for derived and trianguated categories based on the notion of a stable model category, and show how it can be applied to the problem of gluing triangulated categories.
D. Kaledin
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