Author | Fried, Michael D. author |
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Title | Field Arithmetic [electronic resource] / by Michael D. Fried, Moshe Jarden |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1986 |
Connect to | http://dx.doi.org/10.1007/978-3-662-07216-5 |
Descript | XVII, 460 p. 2 illus. online resource |
1. Infinite Galois Theory and Profinite Groups -- 2. Algebraic Function Fields of One Variable -- 3. The Riemann Hypothesis for Function Fields -- 4. Plane Curves -- 5. The ?ebotarev Density Theorem -- 6. Ultraproducts -- 7. Decision Procedures -- 8. Algebraically Closed Fields -- 9. Elements of Algebraic Geometry -- 10. Pseudo Algebraically Closed Fields -- 11. Hilbertian Fields -- 12. The Classical Hilbertian Fields -- 13. Nonstandard Structures -- 14. Nonstandard Approach to Hilbertโs Irreducibility Theorem -- 15. Profinite Groups and Hilbertian Fields -- 16. The Haar Measure -- 17. Effective Field Theory and Algebraic Geometry -- 18. The Elementary Theory of e-free PAC Fields -- 19. Examples and Applications -- 20. Projective Groups and Frattini Covers -- 21. Perfect PAC Fields of Bounded Corank -- 22. Undecidability -- 23. Frobenius Fields -- 24. On ?-free PAC Fields -- 25. Galois Stratification -- 26. Galois Stratification over Finite Fields -- Open Problems -- References