Geometry in dg-categories
WebIn this chapter we recall some basic facts about differential graded (dg) categories. Foramoredetailedtreatmentofdg-categories,see,e.g.,Keller(1994);Keller(2006); Drinfeld … Webspherical 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 …
Geometry in dg-categories
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WebJun 12, 2008 · category of noncommutative spaces we need some preparation on DG categories, which will be quite concise. For details we refer the readers to e.g., [23],[37],[63]. WebMay 1, 2007 · The purpose of this work is to prove the existence of an algebraic moduli classifying objects in a given triangulated category. To any dg-category T (over some base ring k), we define a D −-stack M T in the sense of [Toën B., Vezzosi G., Homotopical algebraic geometry II: Geometric stacks and applications, Mem. Amer. Math. Soc., in …
WebarXiv:math/0106046v2 [math.DG] 18 Jun 2001 Zeros of closed 1-forms, homoclinic orbits, ... Schnirelman category, dependingon a topological space X and a 1-dimensional real cohomology class ξ ∈ H1(X;R). We prove that any closed 1-form ω in class ξ … WebNov 1, 2024 · Since R is a hypersurface, the dg category Sg dg (R) is isomorphic, in the homotopy category of dg categories, to the underlying differential Z-graded category of the differential Z / 2-graded category of matrix factorizations of Q, cf. [9], [24] and Theorem 2.49 of [3]. Thus, it is 2-periodic and so is its Hochschild cohomology.
WebJun 17, 2016 · A prestack is an arbitrary functor from affine schemes to ∞ -groupoids (i.e. spaces in the sense of homotopy theory). For example, affine schemes are … 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 …
WebIn §7, we analyze the dimension of derived categories in algebra and geometry. In §7.1, we use resolution of the diagonal methods. We show that for Aa finite ... category of dg …
epstein brothers carpet west hartford ctWebWhen 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. epstein body picsWebAug 22, 2024 · This also gives a category; one can show that any choices of representatives for two classes in \(H^0(\mathscr {A}(X,Y))\) leads to the same class under composition.. Remark 1. The category \(\mathscr {C}(k)\) of dg k-modules is not itself a dg category, as the morphism spaces are just usual k-modules without any extra … epstein behavioral health centerWebMar 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 epstein bill clinton painting in dragWebMar 27, 2014 · DG-enhancement of its deriv ed category of coherent shea ves is strongly unique. But this uniqueness is too flexible, it allows to lift action onto DG-level only in a very weak sense: epsteinblackbook.com/all-namesWebof 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 … epstein britany f doWebTriangulated categories were invented by J.-L. Verdier in the early sixties as an appropriate language for formulating Grothendieck's duality theory in algebraic geometry. ... we will … epstein brothers flooring west hartford