2008, ISBN: 9783540772699

Gebunden, 820 Seiten, 241mm x 160mm x 49mm, Sprache(n): eng Third revised edition of the classic Ergebnisse volume "Field Arithmetic" by M. Fried and M. JardenImproves the second edition … More...

Gebunden, 820 Seiten, 241mm x 160mm x 49mm, Sprache(n): eng Third revised edition of the classic Ergebnisse volume "Field Arithmetic" by M. Fried and M. JardenImproves the second edition in two ways:1. Removes many typos and mathematical inaccuracies that occur in the second edition (in particular fills a gap in the references)2. Reports on five open problems of the second edition that were solved since that edition appeared in 2005Includes supplementary material: sn.pub/extrasField Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress 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, 1974-1978Associate Professor, Tel Aviv University, 1978-1982Professor, Tel Aviv University, 1982-Incumbent of the Cissie and Aaron Beare Chair, Tel Aviv University. 1998- Academic and Professional AwardsFellowship 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 theMinerva Foundation, 1997-.L. Meitner-A.v.Humboldt Research Prize, 2001Member, Max-Planck Institut f\"ur Mathematik in Bonn, 2001.   Versandkostenfreie Lieferung Absolute Galois Groups, Algebra, Counting, finite fields, Galois Stratification, Hilbertian Fields, Morphism, PAC Fields, Profinite Groups, Variable, Geometry, Number Theory, theorem, Galoistheorie - Galois, Evariste, Zahlentheorie, [PU: Springer, Berlin/Heidelberg]<

2005, ISBN: 9783540772699

Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and… More...

Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements.Progress 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. Buch, Springer / Springer Berlin Heidelberg / Springer, Berlin<

ISBN: 9783540772699

This book uses algebraic tools to study the elementary properties of classes of fields and related algorithmic problems. The first part covers foundational material on infinite Galois the… More...

This book uses algebraic tools to study the elementary properties of classes of fields and related algorithmic problems. The first part covers foundational material on infinite Galois theory, profinite groups, algebraic function fields in one variable and plane curves. It provides complete and elementary proofs of the Chebotarev density theorem and the Riemann hypothesis for function fields, together with material on ultraproducts, decision procedures, the elementary theory of algebraically closed fields, undecidability and nonstandard model theory, including a nonstandard proof of Hilbert's irreducibility theorem. The focus then turns to the study of pseudo algebraically closed (PAC) fields, related structures and associated decidability and undecidability results. PAC fields (fields K with the property that every absolutely irreducible variety over K has a rational point) first arose in the elementary theory of finite fields and have deep connections with number theory. This fourth edition substantially extends, updates and clarifies the previous editions of this celebrated book, and includes a new chapter on Hilbertian subfields of Galois extensions. Almost every chapter concludes with a set of exercises and bibliographical notes. An appendix presents a selection of open research problems. Drawing from a wide literature at the interface of logic and arithmetic, this detailed and self-contained text can serve both as a textbook for graduate courses and as an invaluable reference for seasoned researchers. New Textbooks>Hardcover>Science>Mathematics>Mathematics, Springer Berlin Heidelberg Core >2 >T<

2008, ISBN: 9783540772699

[ED: Gebunden], [PU: Springer Berlin Heidelberg], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Third revised edition of the classic Erg… More...

[ED: Gebunden], [PU: Springer Berlin Heidelberg], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Third revised edition of the classic Ergebnisse volume Field Arithmetic by M. Fried and M. JardenImproves the second edition in two ways: 1. Removes many typo, DE, [SC: 0.00], Neuware, gewerbliches Angebot, Hardcover, 792, [GW: 2900g], 3. Auflage, Banküberweisung, PayPal, [CT: Naturwissenschaft/Mathematik / Sonstiges - Naturwissenschaften]<