Abstract
Let O be an excellent Dedekind ring with perfect residue fields, and let Y = Spec(O). Let C be a curve over Y. (For precise definitions, see §1; we assume C has a smooth geometrically irreducible general fibre, but we do not assume C is regular or complete). In this paper we will prove a relative minimal models Theorem, and a variant due to M. Artin of the Deligne-Mumford stable reduction Theorem. To state these results, let M(C) be the set of regular curves C′ for which there is a proper birational Y-morphism C′ → C. Let ≥ be the partial order on M(C) defined by C′ ≥ C″ if there is a proper morphism C′ → C″ over C.
Both authors are partially supported by MSRI, NSF and Sloan Foundation grants
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Chinburg, T., Rumely, R. (1991). Well-Adjusted Models for Curves over Dedekind Rings. In: van der Geer, G., Oort, F., Steenbrink, J. (eds) Arithmetic Algebraic Geometry. Progress in Mathematics, vol 89. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0457-2_2
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DOI: https://doi.org/10.1007/978-1-4612-0457-2_2
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