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Let Z/K be a non-singular complete curve over a complete valued field K. The uniformization of the Jacobi variety of Z is an extension of a principally polarized abelian variety A(Z), with good reduction, by a torus. Using deformation theory of curves, one shows that A(Z) is in general not a product of Jacobian varieties.

Uniformisation de variétés de Jacobi et déformations de courbes