Semistable Minimal Models of Threefolds in Positive or Mixed Characteristic

Abstract

We extend the minimal model theorem to the 3-dimensional schemes which are projective and have semistable reduction over the spectrum of a Dedekind ring.

21 pages, AMS-Tex. In the revised version, Question 5.8 is replaced by Theorem 5.8

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• On relative rational chain connectedness of threefolds with anti-big canonical divisors in positive characteristics
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• Vanishing on toric surfaces
• Monodromy Criterion for the Good Reduction of K3 Surfaces
• Counter-examples to the minimal model theory in characteristic two
• Flips from 4-folds with isolated complete intersection singularities whose downstairs have rational bi-elephants
• Basepoint freeness for nef and big line bundles in positive characteristic