Michael D. FriedMoshe JardenApril 9, 2008

Springer Science & Business MediaProgress 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.

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.

Education:

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".

Positions:

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.

Publisher

Springer Science & Business Media

Published on

Apr 9, 2008

Pages

792

ISBN

9783540772705

Language

English

Genres

Mathematics / Algebra / Abstract

Mathematics / Algebra / General

Mathematics / General

Mathematics / Geometry / Algebraic

Mathematics / Geometry / General

Mathematics / History & Philosophy

Mathematics / Logic

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