Exterior differential systems via functors of Artin rings

TL;DR

This paper uses functors of Artin rings to establish the existence of universal formal solutions for exterior differential systems, providing tools to analyze their tangent spaces and obstructions.

Contribution

It introduces a novel application of Artin ring functors to exterior differential systems, including the computation of tangent spaces and obstruction theories.

Findings

Proves existence of universal formal solutions.

Computes tangent space of the solution functor.

Analyzes obstruction theory for solutions.

Abstract

We apply the theory of functors of Artin rings to prove the existence of a universal formal solution to a exterior differential system. We compute the tangent space and the obstruction theory of the funtor of Artin ring governing the solutions of the exterior differential system.