Auteurs : Margarida Melo ; Samouil Molcho ; Martin Ulirsch ; Filippo Viviani

In this article we provide a stack-theoretic framework to study the universal tropical Jacobian over the moduli space of tropical curves. We develop two approaches to the process of tropicalization of the universal compactified Jacobian over the moduli space of curves -- one from a logarithmic and the other from a non-Archimedean analytic point of view. The central result from both points of view is that the tropicalization of the universal compactified Jacobian is the universal tropical Jacobian and that the tropicalization maps in each of the two contexts are compatible with the tautological morphisms. In a sequel we will use the techniques developed here to provide explicit polyhedral models for the logarithmic Picard variety.

• 14A21 - Logarithmic algebraic geometry, log schemes
• 14H10 - Families, moduli of curves (algebraic)
• 14H40 - Jacobians, Prym varieties
• 14T15 - Combinatorial aspects of tropical varieties
• 14T20 - Geometric aspects of tropical varieties

• 1 zbMATH Open