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.
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