  The aim of this paper is to present a version of the generalized
Pohozaev-Schoen identity in the context of asymptotically euclidean manifolds.
Since these kind of geometric identities have proven to be a very powerful tool
when analysing different geometric problems for compact manifolds, we will
present a variety of applications within this new context. Among these
applications, we will show some rigidity results for asymptotically euclidean
Ricci-solitons and Codazzi-solitons. Also, we will present an almost-Schur-type
inequality valid in this non-compact setting which does not need restrictions
on the Ricci curvature. Finally, we will show how some rigidity results related
with static potentials also follow from these type of conservation principles.
