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Algebraic Patching de Moshe Jarden

Algebraic Patching: Springer Monographs in Mathematics

Autor Moshe Jarden
en Limba Engleză Hardback – 5 ian 2011
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 $C$.
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Specificații

ISBN-13: 9783642151279
ISBN-10: 3642151272
Pagini: 316
Ilustrații: XXIV, 292 p.
Dimensiuni: 160 x 241 x 22 mm
Greutate: 0.59 kg
Ediția:2011
Editura: Springer
Colecția Springer Monographs in Mathematics
Seria Springer Monographs in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

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.

Notă biografică

Michael D. Fried received his PhD in Mathematics from the University of Michigan in 1967. After postdoctoral research at the Institute for Advanced Study (1967-1969), he became professor at Stony Brook University (8 years), the University of California at Irvine (26 years), the University of Florida (3 years) and the Hebrew University (2 years). He has held visiting positions at MIT, MSRI, the University of Michigan, the University of Florida, the Hebrew University, and Tel Aviv University. He has been an editor of several mathematics journals including the Research Announcements of the Bulletin of the American Mathematical Society and the Journal of Finite Fields and its Applications. His research is primarily in the geometry and arithmetic of families of nonsingular projective curve covers applied to classical moduli spaces using theta functions and l-adic representations. These are especially applied to relating the Regular Inverse Galois Problem and extensions of Serre's Open Image Theorem. He was included in 2013 Class of Fellows of the American Mathematical Society. He was also a Sloan Fellow (1972-1974), Lady Davis Fellow at Hebrew University (1987-1988), Fulbright scholar at Helsinki University (1982-1983), and Alexander von Humboldt Research Fellow (1994-1996). Moshe Jarden received his PhD in Mathematics from the Hebrew University of Jerusalem in 1970 under the supervision of Hillel Furstenberg. His post-doctoral research was completed during the years 1971-1973 at the Institute of Mathematics, Heidelberg University, where he habilitated in 1972. In 1974, he 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. His research focuses on families of large algebraic extensions of Hilbertian fields. His book Field Arithmetic (1986) earned him the Landau Prize in 1987. For his pioneering work, and especially his long term cooperation with German mathematicians, he was awarded the L. Meithner-A.v.Humboldt Prize by the Alexander von Humboldt Foundation in 2001. He is the author of "Algebraic Patching", a Springer Monographs in Mathematics book and a joint author with Dan Haran of another book "The Absolute Galois group of a Semi-Local Fields" of the above-mentioned Springer Monographs in Mathematics.

Textul de pe ultima copertă

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 $C$.

Caracteristici

Develops the method of "algebraic patching" to realize finite groups. Leads to the solution of two central results in "Field Arithmetic". Assumes only basic algebra and Galois theory. Includes supplementary material: sn.pub/extras