Conservation laws and variational sequences in gauge-natural theories

In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable vector density is known to generate the so-called conserved Noether currents. It turns out that along any section of the rel evant gauge-natural bundle this density is the divergence of a skew-symmetr ic tenser density, which is called a superpotential for the conserved curre nts. We describe gauge-natural superpotentials in the framework of finite order variational sequences according to Krupka. We refer to previous results of ours on variational Lie derivatives concerning abstract versions of Noether 's theorems, which are here interpreted in terms of 'horizontal' and 'verti cal' conserved currents. The gauge-natural lift of principal automorphisms implies suitable linearity properties of the Lie derivative operator. Thus abstract results due to Kolar, concerning the integration by parts procedur e, call be applied to prove the existence and globality of superpotentials in a very general setting.