Jarden Algebraic Patching

2011
ISBN: 978-3-642-15128-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 292 Seiten, eBook

Reihe: Springer Monographs in Mathematics

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 $C$ is free of rank equal to the cardinality of $C$.

Zielgruppe

Research

Autoren/Hrsg.

Jarden, Moshe

Inhaltsverzeichnis

1. Algebraic Patching.- 2. Normed Rings.- 3. Several Variables.- 4. Constant Split Embedding Problems over Complete Fields.- 5. Ample Fields.- 6. Non-Ample Fields.- 7. Split Embedding Problems over Complete Fields.- 8. Split Embedding Problems over Ample Fields.- 9. The Absolute Galois Group of C(t).- 10. Semi-Free Profinite Groups.- 11. Function Fields of One Variable over PAC Fields.- 12. Complete Noetherian Domains.- Open Problems.- References.- Glossary of Notation.- Index.

Über Autor(innen)

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.