Buch, Englisch, Band 11, 792 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1379 g
Buch, Englisch, Band 11, 792 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1379 g
ISBN: 978-3-540-77269-9
Verlag: Springer Berlin Heidelberg
Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)?
The third edition improves the second edition in two ways: First it removes many typos and mathematical inaccuracies that occur in the second edition (in particular in the references). Secondly, the third edition reports on five open problems (out of thirtyfour open problems of the second edition) that have been partially or fully solved since that edition appeared in 2005.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Infinite Galois Theory and Profinite Groups.- Valuations and Linear Disjointness.- Algebraic Function Fields of One Variable.- The Riemann Hypothesis for Function Fields.- Plane Curves.- The Chebotarev Density Theorem.- Ultraproducts.- Decision Procedures.- Algebraically Closed Fields.- Elements of Algebraic Geometry.- Pseudo Algebraically Closed Fields.- Hilbertian Fields.- The Classical Hilbertian Fields.- Nonstandard Structures.- Nonstandard Approach to Hilbert’s Irreducibility Theorem.- Galois Groups over Hilbertian Fields.- Free Profinite Groups.- The Haar Measure.- Effective Field Theory and Algebraic Geometry.- The Elementary Theory of e-Free PAC Fields.- Problems of Arithmetical Geometry.- Projective Groups and Frattini Covers.- PAC Fields and Projective Absolute Galois Groups.- Frobenius Fields.- Free Profinite Groups of Infinite Rank.- Random Elements in Profinite Groups.- Omega-Free PAC Fields.- Undecidability.- Algebraically Closed Fields with Distinguished Automorphisms.- Galois Stratification.- Galois Stratification over Finite Fields.- Problems of Field Arithmetic.