Semi-Stable Reduction of Foliations

The content is the minimal model theorem for foliations by curves. It continues the roll-out of the various ingredients in the Green-Griffiths conjecture for algebraic surfaces McQuillan. The result is, however, presented as a self-contained theorem in complex algebraic geometry without foliation dynamics and independent of its motivation. Working familiarity with algebraic champs (the mis-translation stack will be eschewed) is essential. Indices of notation and definitions are provided.