## Wild and even points in global function fields

### Volume 154 / 2018

Colloquium Mathematicum 154 (2018), 275-294
MSC: Primary 11E12; Secondary 11E81, 11G20, 14H05.
DOI: 10.4064/cm6979-1-2018
Published online: 14 September 2018

#### Abstract

We develop a criterion for a point of a 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 necessary.