Dx-Schemes and Jets in Conformal Gravity Using Integral Transforms

Abstract

A scheme is a scheme equipped with a flat connection over a smooth scheme on a base field. The flat connection equipment is a characterization of this scheme to construct through isomorphisms between commutative algebras and formal moduli problems the conformal images of the space-time that are solutions in conformal field theory. If are considered the schemes and their particular tools, the jets, these determine conformal blocks of space-time pieces that are invariant under conformal transformations. These conformal block of space-time pieces determine a homogeneous degree factor that characterizes the solutions in a complex Riemannian model of the space-time of the field equations to certain tensors of the Weyl curvature. Finally, is demonstrated that the algebra belonging to the schemes to the mentioned formal moduli problem is the image under a generalized Penrose transform that in the conformal context of many pieces of the space-time, has a structure as objects in commutative rings of CAlgk each one.