Eivind Eriksen

Computing 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 obstruction theory for this functor in terms of global Hochschild cohomology. An important feature of this obstruction theory is that it can be computed in concrete terms in many interesting cases. In the last part of the paper, we describe noncommutative deformation functors for sheaves and quasi-coherent sheaves of modules on a ringed space

CONNECTIONS ON MODULES OVER SINGULARITIES OF FINITE CM REPRESENTATION TYPE

(X, \mathcal{A})

Computing Noncommutative Global Deformations Of D-Modules

. We show that for any good

Connections on Modules Over Quasi-Homogeneous Plane Curves

\mathcal{A}

Computing Noncommutative Deformations

-affine open cover

Equivariant Lie-Rinehart cohomology

\mathsf{U}

Connections on Modules over Singularities of Finite and Tame CM Representation Type

of

An example of noncommutative deformations 1

X

An introduction to noncommutative deformations of modules

, the forgetful functor

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\mathsf{QCoh}(\mathcal{A}) \to \mathsf{PreSh}(\mathsf{U}, \mathcal{A})