  We address the questions of conservation and integrability of the charges in
two and three-dimensional gravity theories at infinity. The analysis is
performed in a framework that allows us to treat simultaneously asymptotically
locally AdS and asymptotically locally flat spacetimes. In two dimensions, we
start from a general class of models that includes JT and CGHS dilaton gravity
theories, while in three dimensions, we work in Einstein gravity. In both
cases, we construct the phase space and renormalize the divergences arising in
the symplectic structure through a holographic renormalization procedure. We
show that the charge expressions are generically finite, not conserved but can
be made integrable by a field-dependent redefinition of the asymptotic symmetry
parameters.
