2024 Geometry in dg-categories

Geometry in dg-categories

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August undefined, 2024

WebOct 18, 2024 · The framework of dg-categories and dg-functors is too narrow for many problems, and it is preferable to consider the wider class of A ... Serre A ∞ A_\infty functors, talk at Categories in geometry and math. physics, Split 2007, slides, pdf, work with Volodymyr Lyubashenko. The relation of A ... WebTheorem. We then focus our attention on a model category which plays a strong role in algebraic geometry: the category of small dg-categories. After presenting a method of …

Milnor descent for cohesive dg-categories - University of …

WebJul 19, 2024 · Bertrand Toen, section 3 in The homotopy theory of dg-categories and derived Morita theory, arXiv:math/0408337. Paragraph 2.2 of. Dmitri Orlov, Smooth and proper noncommutative schemes and gluing of DG categories, arXiv:1402.7364. Last revised on July 19, 2024 at 21:27:05. WebMar 31, 2024 · Download Citation Geometry in dg-Categories After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists … body flicker technique

Geometry of Derived Categories on Noncommutative …

Webthe central results in the theory of dg-categories that we will use in the proof of our main theorem. This is a consequence of a lemma of Keller (section 7.1 of [Ke]). Lemma 2.3 ‘ Suppose that C and Dare dg-categories, which are full dg-sub-categories of dg-categories C bigand D big,soC C bigand D D big.LetF be a dg-functor from C bigto D WebJan 1, 2010 · The purpose of these four lectures is to provide an introduction to the theory of dg-categories. There are several possible points of view to present the subject, and my … WebThe notion of DG category 78 10.4. The symmetric monoidal structure on DG categories 80 10.5. Compact objects and ind-completions 81 10.6. Change of notations 83 Introduction This Chapter is meant to provide some background on 1-categories and higher algebra (the latter includes the notions of (symmetric) monoidal 1-category, (commutative ... glbjackson.com

Geometric invariant theory and derived categories of …

[math/0503269] Moduli of objects in dg-categories

WebOct 8, 2002 · Keller introduced a notion of quotient of a differential graded category modulo a full differential graded subcategory which agrees with Verdier's notion of quotient of a … Webof categories between derived categories on the noncommutative complex torus and on a holomorphic gerbe on the dual complex torus. Contents 1. Introduction 2 2. The quasi-perfect category of modules over a di erential graded algebra 4 2.1. Review of the perfect DG category of a curved DGA 4 2.2. The Quasi-perfect category 6 2.3. DG … body flex with greer childers dvdWebspherical twist autoequivalences of a dg-category can be obtained from mutation in this manner. Motivated by a prediction from mirror symmetry, we re ne the main theorem describing the derived category of a GIT quotient. We produce additional derived autoequivalences of a GIT quotient and propose an interpretation in terms of monodromy … bodyflight limited

"WebFeb 28, 2014 · In this paper we discuss different properties of noncommutative schemes over a field. We define a noncommutative scheme as a differential graded category of a special type. We study regularity, smoothness and properness for noncommutative schemes. Admissible subcategories of categories of perfect complexes on smooth … " - Geometry in dg-categories

Geometry in dg-categories

WebOct 15, 2024 · Exact DG-categories and fully faithful triangulated inclusion functors. Leonid Positselski. We construct an "almost involution" assigning a new DG-category to a given … WebOct 26, 2024 · I am mostly interested by applications to algebraic geometry. I know basic of category theory, homological algebra, algebraic geometry and a reasonable amount of …

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WebMar 22, 2024 · Geometry in dg-Categories By Maxim Kontsevich Edited by Mathieu Anel , Carnegie Mellon University, Pennsylvania , Gabriel Catren , Centre National de la Recherche Scientifique (CNRS), Paris Webgeometry. The idea of this approach to geometry is to replace all geometric con-structions on a space X by constructions on the dg category of sheaves of modules on X in order …

WebWhen one is talking about geometry from an axiomatic perspective ( you want to talk about points, lines, planes, angles etc.) you are really looking at a model for your axioms. Here we might talk about Euclidean, Riemannian, Hyperbolic, Projective, Spherical and (perhaps) Elliptic geometries. Web1.2. The 2-category of DG categories. We’d like to view the totality of DG categories as an (1;2)-category in 2 ways, denoted DGCat cont and DGCat, respectively, where in both …

http://www.numdam.org/item/10.1016/j.ansens.2007.05.001.pdf Webto a diﬀerential graded (dg in short) category up to a homotopy equivalence, and is Karoubi (e.g. idempotent) closed. The main idea of derived non-commutative algebraic geometry is to treat any Karoubi closed small dg category as the category of perfect complexes on a “space”. By a foundamental result of A. Bondal and M. Van den Bergh, any

Web1.2. The basic notions related to that of DG category are recalled in §2. Let Abe a DG category and B⊂Aa full DG subcategory. Let Atr denote the triangulated category associated to A(we recall its deﬁnition in 2.4). A DG quotient (or simply a quotient) of Amodulo Bis a diagram of DG categories and DG functors (1.1) A←−≈ A˜ →Cξ body flight conceptsWebOct 30, 2016 · The homotopy category K(A,M) of DG A-modules in M. - Localization of categories. The derived category D(A,M), which is the localization of K(A,M) with respect to the quasi-isomorphisms. ... Category Theory (math.CT); Algebraic Geometry (math.AG); K-Theory and Homology (math.KT) MSC classes: 18E30 (Primary) 18G10, 16E45 ( … bodyflight equipmentWebJan 8, 2024 · PDF This is a review of a review of Kontsevich, Maxim Geometry in dg-categories. (English) Zbl 07425824 Anel, Mathieu (ed.) et al., New spaces in... Find, … bodyflight associationWebSep 30, 2024 · Title: Homotopy colimit of dg categories, wrapped Fukaya categories, and lens spaces; Abstract: Ganatra, Pardon, and Shende introduced a way to compute wrapped Fukaya categories of Weinstein domains by taking the homotopy colimit of wrapped Fukaya categories of their sectorial coverings. However, homotopy colimits are hard to compute … glb iphoneWebA DG-category with one object is the same as a DG-ring. A DG-ring over a field is called DG-algebra, or differential graded algebra. Further properties. The category of small dg … glbl early birdWebpart I will introduce the homotopy category of dg-categories, and propose it as a setting in order to deﬁne a better behaved localization construction. This homotopy category of … bodyflight bottropWebNov 12, 2014 · Metaplectic Whittaker category and quantum groups: the "small" FLE (an "official" paper, joint with S.~Lysenko, last updated March 8, 2024) On factorization … bodyflight barn