120 Pages
by
A K Peters/CRC Press
120 Pages
by
A K Peters/CRC Press
Also available as eBook on:
This 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... Read more
Foreword, 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, Bibliography
Biography
Jean-Pierre Serre
" is a very stimulating text, which . . . will attract mathematicians working in group theory, number theory, algebraic geometry, and complex analysis.
—Zentralblatt für 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"
