Noncommutative deformations of modules
نویسندگان
چکیده
منابع مشابه
Noncommutative Deformations of Sheaves of Modules
Let k be an algebraically closed field, let X be a topological space, let A be a sheaf of associative k-algebras on X, and let F = {F1, . . . ,Fp} be a finite family of sheaves of left A-modules on X. In this paper, we develop a noncommutative deformation theory for the family F . This theory generalizes the noncommutative deformation theory for finite families of left modules over an associati...
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Let (X,D) be a D-scheme in the sense of Beilinson and Bernstein, given by an algebraic variety X and a morphism OX → D of sheaves of rings on X. We consider noncommutative deformations of quasi-coherent sheaves of left D-modules on X, and show how to compute their pro-representing hulls. As an application, we compute the noncommutative deformations of the left DX -module OX when X is any ellipt...
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Let k be an algebraically closed (commutative) field, let A be an associative k-algebra, and let M = {M1, . . . , Mp} be a finite family of left A-modules. We study the simultaneous formal deformations of this family, described by the noncommutative deformation functor DefM : ap → Sets introduced in Laudal [8]. In particular, we prove that this deformation functor has a pro-representing hull, a...
متن کاملNoncommutative Deformations of Sheaves and Presheaves of Modules
We work over an algebraically closed field k, and consider the noncommutative deformation functor DefF of a finite family F of presheaves of modules defined over a presheaf of k-algebras A on a small category c. We develop an obstruction theory for DefF , with certain global Hochschild cohomology groups as the natural cohomology. In particular, we show how to calculate the prorepresenting hull ...
متن کاملComputing Noncommutative Deformations of Presheaves and Sheaves of Modules
We describe a noncommutative deformation theory for presheaves and sheaves of modules that generalizes the commutative deformation theory of these global algebraic structures, and the noncommutative deformation theory of modules over algebras due to Laudal. In the first part of the paper, we describe a noncommutative deformation functor for presheaves of modules on a small category, and an obst...
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ژورنال
عنوان ژورنال: Homology, Homotopy and Applications
سال: 2002
ISSN: 1532-0073,1532-0081
DOI: 10.4310/hha.2002.v4.n2.a17