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OverviewThis book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt construction for p-groups, p != 2, as well as Hilbert's irreducibility theorem and the large sieve inequality, are presented. The second half is devoted to rationality and rigidity criteria and their application in realizing certain groups as Galois groups of regular extensions of Q(T). While proofs are not carried out in full detail, the book contains a number of examples, exercises, and open problems. Full Product DetailsAuthor: Jean-Pierre SerrePublisher: Taylor & Francis Inc Imprint: A K Peters Edition: 2nd edition Dimensions: Width: 15.20cm , Height: 1.50cm , Length: 22.90cm Weight: 0.317kg ISBN: 9781568814124ISBN 10: 1568814127 Pages: 120 Publication Date: 02 November 2007 Audience: College/higher education , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of ContentsForeword, Notation, Introduction, 1 Examples in low degree, 2 Nilpotent and solvable groups as Galois groups over Q, 3 Hilbert’s irreducibility theorem, 4 Galois extensions of Q(T): first examples, 5 Galois extensions of Q(T) given by torsion on elliptic curves, 6 Galois extensions of C(T), 7 Rigidity and rationality on finite groups, 8 Construction of Galois extensions of Q(T) by the rigidity method, 9 The form Tr(x2) and its applications, 10 Appendix: the large sieve inequality, BibliographyReviewsis a very stimulating text, which ... will attract mathematicians working in group theory, number theory, algebraic geometry, and complex analysis. --Zentralblatt fur Mathematik This small book contains a nice introduction to some classical highlights and some recent work on the inverse Galois theory problem. The topics and main theorems are carefully chosen and composed in a masterly manner. --Mathematiacl Reviews -July 2007 Serre had the great good sense to have notes taken at his 1988 lectures at Harvard, creating a slim volume of great interest... -BOOK NEWS Inc., June 2008 J.-P. Serre, one of the greatest mathematicians in our time, provides here a unique introduction to both some classical milestones and some recent developments in the realm of inverse Galois theory. ... [This book] will maintain its unique, unparalleled role in the literature on inverse Galois theory for further generations. Now as before, J.-P. Serre's masterpiece of expository writing is an unvaluable source of inspiration and incitement likewise. -Werner Kleinert, Zentralblatt MATH, January 2007 Serre's book helped to call the attention to a deep classical problem with connections to algebraic geometry, topology, algebra, and number theory. By carefully selecting examples, methods and topics, this book goes deeply into the problem. -MAA Reviews, September 2008 ... This is a very stimulating text, which... will attract mathematicians working in group theory, number theory, algebraic geometry, and complex analysis. - Zentralblatt fur Mathematik This small book contains a nice introduction to some classical highlights and some recent work on the inverse Galois theory problem. The topics and main theorems are carefully chosen and composed in a masterly manner. - Mathematical Reviews Author InformationJean-Pierre Serre is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory, and topology. He has received numerous awards and honors for his mathematical research and exposition, including the Fields Medal in 1954 and the Abel Prize in 2003. Tab Content 6Author Website:Countries AvailableAll regions |
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