Lagrangian formalism and the intrinsic geometry of PDEs

A notion of internal Lagrangian for a system of differential equations is introduced. A spectral sequence related to internal Lagrangians is obtained. A connection between internal Lagrangians and presymplectic structures is investigated. An interpretation of the term $E_2^{3,n-2}$ of Vinogradov’s $\mathcal{C}$-spectral sequence is given for irreducible gauge theories.