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We develop the Batalin-Vilkovisky formalism for classical field theory ongeneric globally hyperbolic spacetimes. A crucial aspect of our treatment isthe incorporation of the principle of local covariance which amounts toformulate the theory without reference to a distinguished spacetime. Inparticular, this allows a homological construction of the Poisson algebra ofobservables in classical gravity. Our methods heavily rely on the differentialgeometry of configuration spaces of classical fields.

Batalin-Vilkovisky formalism in the functional approach to classical field theory