A N\'eron model of the universal jacobian

Abstract

The jacobian of the universal curve over $\mathcal{M}_{g,n}$ is an abelian scheme over $\mathcal{M}_{g,n}$. Our main result is the construction of an algebraic space $\beta\colon \tilde{\mathcal{M}}_{g,n} \rightarrow \bar{\mathcal{M}}_{g,n}$ over which this jacobian admits a N\'eron model, and such that $\beta$ is universal with respect to this property. We prove certain basic properties, for example that $\beta$ is separated, locally of finite presentation, and satisfies a certain restricted form of the valuative criterion for properness. In general, $\beta$ is not quasi-compact. We relate our construction to Caporaso's balanced Picard stack $\mathcal{P}_{d,g}$.