In this chapter we review the construction by Lichtenbaum  and Shafare-vitch  of relatively minimal and minimal models of curves over Dedekind rings. We have clpsely followed Lichtenbaum ; some proofs have been skipped or summarized so as to go into more detail concerning other parts of the construction. Since the main arguments of  apply over Dedekind rings, we work always over Dedekind rings rather than discrete valuation rings.
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