Ekedahl, Torsten Foliations and inseparable morphisms. (English) Zbl 0659.14018 Algebraic geometry, Proc. Summer Res. Inst., Brunswick/Maine 1985, part 2, Proc. Symp. Pure Math. 46, No. 2, 139-149 (1987). [For the entire collection see Zbl 0626.00011.] The author proves a number of characterizations of groupoid schemes and formal equivalence relations in terms of Lie algebras in positive characteristic. He then introduces foliations as certain sheaves of differential operators on a smooth variety and relates them to groupoid schemes. These techniques are applied to obtain the following results:(1) the Albanese map of a surface of non-positive Kodaira dimension is separable if its image is two-dimensional; (2) a minimal surface in characteristic p is either uniruled or satisfies \(-c_ 2\cdot (p-1)^ 2\leq p\cdot c^ 2_ 1\). Reviewer: F.Herrlich Cited in 1 ReviewCited in 12 Documents MathOverflow Questions: How to visualize the Frobenius endomorphism? MSC: 14G15 Finite ground fields in algebraic geometry 14B25 Local structure of morphisms in algebraic geometry: étale, flat, etc. 14L99 Algebraic groups Keywords:inseparable morphism; groupoid schemes; formal equivalence relations; positive characteristic; foliations; sheaves of differential operators; Albanese map; minimal surface Citations:Zbl 0626.00011 PDF BibTeX XML OpenURL