Generic fibers and descent give another way to understand the composition law. The positive-characteristic part isolates the role of Frobenius. Read this alongside Divisibility of Separated Polynomials.
Background
Galois theory and polynomials in positive characteristic.
Read the full exposition
The complete argument is available as a PDF.
Revision history ·
Revised September 22, 2026: clarified the nontriviality conditions in the closing reducibility discussion and the remainder argument when the outer polynomial is zero. The composition theorem and its hypotheses are unchanged. The PDF and TeX source agree.