Why the Example I'm Reading Makes No Sense

The options, from least to most likely:


1. The author has made a mistake, and his example is merely a house of cards. Extremely unlikely, as this is a well-respected mathematician publishing in a well-respected journal. And one of the purposes of this paper was to correct an error in a similar example from 20+ years ago.


2. I have forgotten something important about rational function fields, Laurent polynomials, twisted extensions, or localizations.


3. We are in characteristic p. Nothing makes sense in characteristic p.