Volume 4 (2021)
Holmes, David
A Néron model of the universal jacobian
Annales Henri Lebesgue, Volume 4 (2021), pp. 1727-1766.

Metadata

DOI10.5802/ahl.115
Keywords Néron models, jacobians, moduli of curves

Abstract

Jacobians of degenerating families of curves are well-understood over 1-dimensional bases due to work of Néron and Raynaud; the fundamental tool is the Néron model and its description via the Picard functor. Over higher-dimensional bases Néron models typically do not exist, but in this paper we construct a universal base change ℳ ˜ g,n →ℳ ¯ g,n after which a Néron model N g,n /ℳ ˜ g,n of the universal jacobian does exist. This yields a new partial compactification of the moduli space of curves, and of the universal jacobian over it. The map ℳ ˜ g,n →ℳ ¯ g,n is separated and relatively representable. The Néron model N g,n /ℳ ˜ g,n is separated and has a group law extending that on the jacobian. We show that Caporaso’s balanced Picard stack acquires a torsor structure after pullback to a certain open substack of ℳ ˜ g,n .


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