4 papers
Gelfand-Fuks cohomology of vector fields on algebraic varieties
Yuly Billig, Kathlyn Dykes
For an affine algebraic variety, we introduce algebraic Gelfand-Fuks cohomology of polynomial vector fields with coefficients in differentiable -modules. Its complex is given b…
A universal sheaf of algebras governing representations of vector fields on quasi-projective varieties
Yuly Billig, Colin Ingalls
We construct a quasi-coherent sheaf of associative algebras which controls a category of -modules over a smooth quasi-projective variety. We establish a local structure theorem…
Differentiable holonomic -modules
Yuly Billig, Henrique Rocha
We study differentiable holonomic sheaves of -modules on a smooth quasi-projective variety. We show that a simple differentiable holonomic sheaf of -modules is locally…
Holonomic -modules for the affine space
Yuly Billig, Henrique Rocha
We study the growth of representations of the Lie algebra of vector fields on the affine space that admit a compatible action of the polynomial algebra. We establish the Bernstein…