Derived Moduli Spaces of Nonlinear PDEs II: Variational Tricomplex and BV Formalism

This paper is the second in a series of works dedicated to studying non-linear partial differential equations via derived geometric methods. We study a natural derived enhancement of the de Rham complex of a non-linear PDE via algebro-geometric techniques and examine its consequences for the functional differential calculus on the space of solutions. Applications to the BV-formalism with and without boundary conditions are discussed.