8 March 2000.

Boris Kruglikov "Formal integrability of differential equations and Weyl tensors".

We introduce the fundamental forms of jet-spaces. We do similar constructions for the equations and derive the Weyl tensor, which belongs to the second cohomology group of the corresponding Spencer sequence. It serves as an obstruction to formal integrability of differential equations. This tensor can be considered as an essential part of the curvature tensor of the Cartan distribution on the equation. We calculate Weyl tensor for some examples and obtain formal/smooth integrability criteria for some types of differential equations.