  We prove that potential conservation laws have characteristics depending only
on local variables if and only if they are induced by local conservation laws.
Therefore, characteristics of pure potential conservation laws have to
essentially depend on potential variables. This statement provides a
significant generalization of results of the recent paper by Bluman, Cheviakov
and Ivanova [J. Math. Phys., 2006, V.47, 113505]. Moreover, we present
extensions to gauged potential systems, Abelian and general coverings and
general foliated systems of differential equations. An example illustrating
possible applications of proved statements is considered. A special version of
the Hadamard lemma for fiber bundles and the notions of weighted jet spaces are
proposed as new tools for the investigation of potential conservation laws.
