Plane Frobenius sandwiches

Plane Frobenius sandwiches of degree $p$

“…The fact that the result holds when k is algebraically closed was proved by Ganong in [4]; we will refer to that fact as Ganong's theorem, and will make use of it in our proof. It was also known that Ganong's argument could prove the result under the weaker assumption that k is a perfect field, but apparently the general case was not known.…”

“…The method used in [4] (namely, the HN-expansions, see [5]) is not available in the general case, because one has to deal with curves with a possibly nonrational place at infinity. The main ingredient in our proof (besides Ganong's theorem) is a result on pairs of polynomials in one indeterminate over an integral domain of positive characteristic (Proposition 1.2), to which the first section is devoted.…”