A regular projective surface S over a field k of char p≥7 with H^0(S,O_S)=k and -K_S nef is geometrically integral over k.
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Geometric singularities of regular surfaces with nef anti-canonical divisors over imperfect fields
A regular projective surface S over a field k of char p≥7 with H^0(S,O_S)=k and -K_S nef is geometrically integral over k.