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Given a finite, flat morphism between embeddable noetherian schemes of puredimension 1, we define the notion of direct and inverse image for generalizeddivisors and generalized line bundles. In the case when we deal with (possiblyreducible, non-reduced) projective curves over a field and the codomain curveis smooth, we introduce the compactified Jacobians parametrizing torsion-freerank-1 sheaves and we study the Norm and inverse image maps betweencompactified Jacobians. Finally, we introduce and study the Prym stack definedas the kernel of the Norm map.

The direct image of generalized divisors and the Norm map between compactified Jacobians