  Surface charges of a $p$-form theory on the boundary of an AdS$_{d+1}$
spacetime are computed. Counter-terms on the boundary produce divergent
corner-terms which holographically renormalize the symplectic form. Different
choices of boundary conditions lead to various expressions for the charges and
the associated fluxes. With the usual standard AdS boundary conditions, there
are conserved zero-mode charges. Moreover, we explore two leaky boundary
conditions which admit an infinite number of charges forming an Abelian algebra
and non-vanishing flux. Finally, we discuss magnetic $p$-form charges and
electric/magnetic duality.
