Spencer cohomology

Summary

Spencer cohomology is a family of cohomology groups attached to the symbol of a system of linear or nonlinear partial differential equations. It is computed from the Spencer complex, an algebraic analogue of the de Rham complex built from polynomials and exterior forms. It measures the obstructions to solving a system order by order in formal power series. It also gives an algebraic criterion for involutivity in the sense of Cartan. The name also refers to a related sheaf cohomology, introduced by D. C. Spencer. It is the cohomology of a manifold with coefficients in the sheaf of solutions of a linear differential operator.