Algebraic Patching - Moshe Jarden

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Résumé :
Assuming only basic algebra and Galois theory, the book develops the method of algebraic patching to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over ample fields. Among others, it leads to the solution of two central results in Field Arithmetic: (a) The absolute Galois group of a countable Hilbertian pac field is free on countably many generators; (b) The absolute Galois group of a function field of one variable over an algebraically closed field dollarsC dollars is free of rank equal to the cardinality of dollarsC dollars.

Biographie:
Moshe Jarden is professor emeritus at the School of Mathematics, Tel Aviv University. He obtained his PhD at the Hebrew University, Jerusalem, in 1970, and his Habilitation at Heidelberg University in 1972, where he was a post doc until 1974, before joining Tel Aviv University. He was awarded the L. Meitner-A.v. Humboldt prize in 2001 for his achievements in mathematics. He is the author of two books, Field Arithmetic (for which he was awarded the Landau Prize in 1987) and Algebraic Patching, and he has published 120 research articles. His research is primarily on field arithmetic. Dan Haran is a professor at the School of Mathematics, Tel Aviv University, where he obtained his PhD in 1983. He was a research fellow at the Mathematical Institute in Erlangen (1983-1986), a visiting assistant professor at Rutgers (1985-1986), a senior lecturer at Tel Aviv University (1986-1991), and a fellow at the Hebrew University (1991-1992) and at the Max-Planck-Institut,Bonn (1992-1993) before joining Tel Aviv University in 1991 as an associate professor, becoming full professor in 2000. His research is in field arithmetic, Galois theory and profinite groups....

Sommaire:
Moshe Jarden was born in 1942 in Tel Aviv, Israel. In 1970 he received his Ph.D in Mathematics from the Hebrew University of Jerusalem having Hillel Furstenberg as his thesis advisor. He spent three years (1972-1974) at the Mathematisches Institut of Heidelberg with Peter Roquette as his mentor and habilitated there in 1972. The years he spent in Heidelberg laid the foundation to a long termed cooperation with German mathematicians, especially with Peter Roquette, Wulf-Dieter Geyer, Gerhard Frey, and Juergen Ritter. As a token to his achievements in Mathematics and his fruitful cooperation with German mathematicians the Alexander von Humboldt Foundation granted Jarden in 2001 the L. Meithner-A.v.Humboldt Prize. In the autumn of 1974 Jarden returned to Israel and joined the School of Mathematics of Tel Aviv University, where he became a full professor in 1982 and the incumbent of the Cissie and Aaron Beare chair in Algebra and Number Theory in 1998. Jointly with Michael Fried, Jarden published the book Field Arithmetic in the series Ergebnisse der Mathematik und ihrer Grenzgebiete of Springer. He won the Landau Prize for the publication of that book. Moshe Jarden inherited his love to Mathematics from his father Dr. Dov Jarden who was both a Hebrew linguistic and a mathematician. He is married to Rina, has three daughters Kmeha, Hemyat, and Uri, and a son Guy. He also has thirteen grandchildren and lives in Mevasseret Zion, near Jerusalem....