Abstract
We provide foundations for a characteristic free study of foliated varieties in terms of infinitesimal actions of formal groupoids. The ultimate goal is the bi-rational geometry of the same, and to this end we prove a cone theorem for foliations in curves, together with structure theorems for extremal rays, and, of course, a minimal model theorem for surfaces. All possible wild ramification effects of Deligne–Mumford champ are built in, along with the occasional use of Artin champ to address the mathbb Q-Gorenstein condition.
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