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Jan 25, 2010 at 22:15 comment added Qing Liu James: I wonder how to prove the Néron model does not exit in your example. The idea of blowing-up the base is nice. There is a paper by J. de Jong and Oort on extending families of stable curves. However it not clear whether Néron model will exists even with alteration (à la de Jong) of $S$.
Jan 25, 2010 at 20:39 comment added Clark Barwick You beat me to it! Nice.
Jan 25, 2010 at 20:35 history answered JBorger CC BY-SA 2.5