Engineering↗
Discriminants and Integral Bases
The discriminant of a basis, the field discriminant, and the index-squared relation that governs maximal order computation.
Every page in the KEVOS library tagged ramification. 4 pages.
The discriminant of a basis, the field discriminant, and the index-squared relation that governs maximal order computation.
Using Newton polygons to decompose primes locally, handling the cases where factoring modulo p is insufficient.
Finding roots in p-adic fields by lifting, and reading ramification structure off the Newton polygon of a polynomial.
How rational primes factor in the maximal order, ramification indices and residue degrees, and the degree relation that constrains them.