Abstract
Let f:X→Sbe a projective morphism of Noetherian schemes. We assume fpurely of relative dimension dand finite Tor-dimensional. We associate to d+1 invertible sheaves \(L{\text{,}}...{\text{,}}L_{d + 1}\)on Xa line bundle IX/S(\(L{\text{,}}...{\text{,}}L_{d + 1}\)) on Sdepending additively on the \(L_{\text{1}}\), commuting to ‘good’ base changes and which represents the integral along the fibres of fof the product of the first Chern classes of the \(L_{\text{1}}\). If d=0, IX/S(\(L\)) is the norm NX/S(\(L\)).
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