The goal of this book is to lead the reader to an understanding of recent results on the Inverse Galois Problem. Assuming only elementary algebra and complex analysis, the author develops the necessary background from topology, Riemann surface theory and number theory.
The goal of this book is to lead the reader to an understanding of recent results on the Inverse Galois Problem. Assuming only elementary algebra and complex analysis, the author develops the necessary background from topology, Riemann surface theory and number theory.
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.
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.
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