Moshe Jarden
 | This article includes a list of general references, but it remains largely unverified because it lacks sufficient corresponding inline citations. (November 2015) |
Moshe Jarden | |
|---|---|
 Moshe Jarden at the Oberwolfach Research Institut for Mathematics. This picture was taken during "The Arithmetic of Fields" 2006 Workshop (source MFO). | |
| Born | 23 August 1942 |
| Nationality | Israeli |
| Known for | Field arithmetics, notably ample fields |
| Awards | Landau prize, L. Meithner-A.v. Humboldt Prize |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Tel Aviv University |
| Doctoral advisor | Prof. H. Furstenberg |
Moshe Jarden (Hebrew: משה ירדן) is an Israeli mathematician, specialist in field arithmetic.
Biography[]
Moshe Jarden was born in 1942 in Tel Aviv. His father, Dr. Dov Jarden, was a mathematician, writer and linguist, who transmitted him his love to mathematics. In 1970 he received his Ph.D in Mathematics from the Hebrew University of Jerusalem, with Hillel Furstenberg as his thesis advisor. He accomplished his post doctorate during the years 1971-1973 at the Institut of Mathematics, Heidelberg University, with Peter Roquette as his mentor, and habilitated there in 1972. During these years in Heidelberg, he initiated an intense and long term cooperation with German mathematicians, especially with Peter Roquette, Wulf-Dieter Geyer, Gerhard Frey, and Juergen Ritter. His achievements in mathematics, as well as the foundation of this fruitful cooperation with German mathematicians, earned him the L. Meithner-A.v.Humboldt Prize by the Alexander von Humboldt Foundation in 2001. In 1974, Moshe Jarden returned to Israel, and joined the School of Mathematics of Tel Aviv University. He became a full professor in 1982, and the incumbent of the Cissie and Aaron Beare chair in Algebra and Number Theory in 1998. One of his great achievements is the publication of the book "Field Arithmetic" in the series Ergebnisse der Mathematik und ihrer Grenzgebiete of Springer, which earned him the Landau Prize.
Work[]
The main contribution of Moshe Jarden in algebra, and in mathematics in general, is his research on families of large algebraic extensions of Hilbertian fields (in particular global fields), parametrized by the automorphisms of the absolute Galois group of the base field. Notable results in this domain are the zero theorem, the transfer theorem, the free generators theorem, the Frey-Jarden theorem about the rank of algebraic varieties over large algebraic fields, Geyer-Jarden theorem about torsion points on elliptic curves over large algebraic fields, and the strong approximation theorem over such fields.
The remarkable development of Galois theory over a class of large fields, called ample fields,[1] is described in the second book of Jarden: Algebraic Patching.[2]
Field arithmetic[]
In 1979, Moshe Jarden came to Irvine and met Michael Fried. This was during this visit that Fried suggested to write a joint book on the topics they had worked about so far, and proposed the name "Field arithmetic".
This book,[3] where Diophantine fields are explored through their absolute Galois groups, was influential in the domain of field theory. Owing to this work, the intense activity of Moshe Jarden, and his influence on his colleagues, "Field Arithmetic" has become a recognized name of a branch of algebra, with its own classification number (12E30 Field Arithmetic). The impact of this book can also be measured by the number of open problems presented in the first and second editions (twenty two), which were mostly solved between the publication of the first and third editions.
In 1987, Moshe Jarden won the Landau Prize for the publication of "Field Arithmetic". Some years after the release of the first edition, it was realized that the term "field arithmetic" had already been coined by the mathematician Paulo Ribenboim somewhat earlier, who had published a book in French named "L'Arithmétique des Corps".
Awards and honors[]
He was awarded the Landau prize for the book "Field Arithmetic" in 1987, and the L. Meithner-A.v.Humboldt Prize in 2001 for his achievements in mathematics.
Selected articles[]
- Moshe Jarden, Elementary statements over large algebraic fields, Transactions of the American Mathematical Society 164 (1972), 67-91.
- Gerhard Frey and Moshe Jarden, Approximation theory and the rank of abelian varieties over large algebraic fields, Proceedings of the London Mathematical Society 28 (1974), 112-128.
- M. Jarden, Algebraic extensions of finite corank of Hilbertian fields, Israel Journal of Mathematics 18 (1974), 279-307.
- W.-D. Geyer and M. Jarden, Torsion points of elliptic curves over large algebraic extensions of finitely generated fields, Israel Journal of Mathematics 31 (1978), 157-197.
- M. Jarden and U. Kiehne, The elementary theory of algebraic fields of finite corank, Inventiones Mathematicae 30 (1975), 275-294.
- M. Fried, D. Haran, and M. Jarden, Galois stratification over Frobenius fields, Advances in Mathematics, 51 (1984), 1-35.
- D. Haran and M. Jarden, The absolute Galois group of a pseudo p-adically closed field, Journal für die reine und angewandte Mathematik 383 (1988), 147-206.
- W.-D. Geyer and M. Jarden, On stable fields in positive characteristic, Geometriae Dedicata 29 (1989), 335-375.
- M. Jarden, Large normal extensions of Hilbertian fields, Mathematische Zeitschrift 224 (1997), 555-565.
- D. Haran and M. Jarden, Regular split embedding problems over complete valued fields, Forum Mathematicum 10 (1998), 329-351.
- D. Haran, M. Jarden, and F. Pop, The absolute Galois group of subfields of the field of totally S-adic numbers, Functiones et Approximatio Commentarii Mathematici, 46 (2012), 205-223.
- M. Jarden, Diamonds in torsion of Abelian varieties, Journal of the Institute of Mathematics Jussieu 9 (2010), 477-480.