Abstract
In this paper, we study the ordinarity of an isotrivial elliptic surface defined over a field of positive characteristic. If an isotrivial elliptic fibration π : X → C is given, X is ordinary when the common fiber of π is ordinary and a certain finite cover of the base C is ordinary. By this result, we may obtain the ordinary reduction theorem for some kinds of isotrivial elliptic surfaces defined over a number field.
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