Explores Galois theory fundamentals, including separable elements, decomposition fields, and Galois groups, emphasizing the importance of finite degree extensions and the structure of Galois extensions.
Covers the proof of Hensel's Lemma and a review of field theory, including Newton's approximation and p-adic complex numbers.
Covers the concept of finite degree extensions in Galois theory, focusing on separable extensions.
Covers the algebraic closure of Qp and the definition of p-adic complex numbers, exploring roots' continuous dependence on coefficients.
Explores the Galois theory of Qp, covering algebraic extensions, inertia groups, and cyclic properties.
Covers the fundamentals of algebraic geometry, including algebraic numbers and irreducible polynomials.
