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It was proved by Tien-Cuong Dinh and me that there is a smooth complexprojective surface whose automorphism group is discrete and not finitelygenerated. In this paper, we will show that there is a smooth projectivesurface, birational to some K3 surface, such that the automorphism group isdiscrete and not finitely generated, over any algebraically closed field of oddcharacteristic except precisely an algebraic closure of the prime field.

A surface in odd characteristic with discrete and non-finitely generated automorphism group