Néron models and compactified Picard schemes over the moduli stack of stable curves

We construct modular Deligne-Mumford stacks representable over parametrizing Néron models of Jacobians as follows. Let B be a smooth curve and K its function field, let be a smooth genus-g curve over K admitting stable minimal model over B. The Néron model → B is then the base change of via the moduli map B → of f , i.e.: B. Moreover is compactified by a Deligne-Mumford stack over , giving a completion of Néron models naturally stratified in terms of Néron models.