Boundary structure of gauge and matter fields coupled to gravity

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.