The paper claims persistence of extendable Galois points under prime reduction for all but finitely many primes, with a quartic classification, but the inner persistence theorem rests on an invalid inference about the open set U.
Fukasawa, On the number of Galois points for a plane curve in positive characteristic
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Persistence of Galois property of hypersurfaces over algebraic integers across other characteristics
The paper claims persistence of extendable Galois points under prime reduction for all but finitely many primes, with a quartic classification, but the inner persistence theorem rests on an invalid inference about the open set U.