An arithmetic variant of Raynaud's theorem

Abstract

It is well known that for a regular semistable curve $\mathfrak{X}$ over a DVR with algebraically closed residue field, the spanning trees of the dual graph of the special fiber of $\mathfrak{X}$ are in bijection with components of the special fiber of the Néron model of the Jacobian of $\mathfrak{X}$. We prove a generalization of this fact that does not require the residue field to be algebraically closed, using a combinatorially enriched version of the dual graph to encode arithmetic information about divisors on $\mathfrak{X}$.

References updated and exposition improved; main results unchanged