We develop a criterion for a point of global function field to be a unique wild point of some self-equivalence of this field. We show that this happens if and only if the class of the point in the Picard group of the field is 2-divisible. Moreover, given a finite set of points, whose classes are 2-divisible in the Picard group, we show that there is always a self-equivalence of the field for which this is precisely the set of wild points. Unfortunately, for more than one point this condition is no longer a necessary one.

We describe the structure of the Witt group W S K of any Hasse domain S K of a global field K by explicitly determining its cyclic direct summands and generators of each such summand. Using this description we find a sufficient condition for the existence of Witt ring isomorphism W S K ∼ = W S L . We give also the necessary and sufficient condition for the existence of Witt ring isomorphism WK → WL of global fields K and L mapping the Witt ring W S K onto the Witt ring W S L .

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