Structures du cube et fibres d'intersection

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We define the notion of a hypercube structure on a functor between two strictly commutative Picard categories which generalizes the notion of a cube structure on a Gₘ-torsor over an abelian scheme. We use this notion to define the intersection bundle of n+1 line bundles on a relative scheme X/S of relative dimension n and to construct an additive structure on the functor Iₓ/ₛ:PIC(X/S)ⁿ⁺¹ PIC(S). Finally, we study a section of Iₓ/ₛ(L₁,...,Lₙ₊₁) which generalizes the resultant of n+1 polynomials in n variables and we interprete some classical formulas with this formalism.