Ebook: Groups as Galois Groups: An Introduction

Part 1. The Basic Rigidity Criteria: 1. Hilbert's irreducibility theorem; 2. Finite Galois extensions of C (x); 3. Descent of base field and the rigidity criterion; 4. Covering spaces and the fundamental group; 5. Riemann surfaces and their functional fields; 6. The analytic version of Riemann's existence theorem; Part II. Further Directions: 7. The descent from C to k; 8. Embedding problems: braiding action and weak rigidity; Moduli spaces for covers of the Riemann sphere; Patching over complete valued fields