Field Arithmetic

Field Arithmetic

by Michael D. Fried, Moshe Jarden



Product Details

ISBN-13: 9783540228110
Publisher: Springer-Verlag New York, LLC
Publication date: 11/28/2004
Series: Ergebnisse Der Mathematik Und Ihrer Gren
Edition description: REV
Pages: 780
Product dimensions: 6.10(w) x 9.25(h) x (d)

About the Author

Moshe Jarden (revised and considerably enlarged the book in 2004 (2nd edition) and revised again in 2007 (the present 3rd edition).

Born on 23 August, 1942 in Tel Aviv, Israel.

Ph.D. 1969 at the Hebrew University of Jerusalem on
"Rational Points of Algebraic Varieties over Large Algebraic Fields".
Thesis advisor: H. Furstenberg.
Habilitation at Heidelberg University, 1972, on
"Model Theory Methods in the Theory of Fields".

Dozent, Heidelberg University, 1973-1974.
Seniour Lecturer, Tel Aviv University, 1974-1978
Associate Professor, Tel Aviv University, 1978-1982
Professor, Tel Aviv University, 1982-
Incumbent of the Cissie and Aaron Beare Chair,
Tel Aviv University. 1998-

Academic and Professional Awards
Fellowship of Alexander von Humboldt-Stiftung in Heidelberg, 1971-1973.
Fellowship of Minerva Foundation, 1982.
Chairman of the Israel Mathematical Society, 1986-1988.
Member of the Institute for Advanced Study, Princeton, 1983, 1988.
Editor of the Israel Journal of Mathematics, 1992-.
Landau Prize for the book "Field Arithmetic". 1987.
Director of the Minkowski Center for Geometry founded by the
Minerva Foundation, 1997-.
L. Meitner-A.v.Humboldt Research Prize, 2001
Member, Max-Planck Institut f\"ur Mathematik in Bonn, 2001.

Table of Contents

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 Free Profinite Groups. - Omega-Free PAC Fields. - Undecidability. - Algebraically Closed Fields with Distinguished Automorphisms. - Galois Stratification. - Galois Stratification over Finite Fields. - Problems of Finite Arithmetic.

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