  The boundary structure of $3+1$-dimensional gravity (in the Palatini-Cartan
formalism) coupled to to gauge (Yang-Mills) and matter (scalar and spinorial)
fields is described through the use of the Kijowski-Tulczijew construction. In
particular, the reduced phase space is obtained as the reduction of a
symplectic space by some first class constraints and a cohomological
description (BFV) of it is presented.
