Topics in Galois Theory: 01 (Research Notes in Mathematics) - Hardcover

Serre, Jean-Pierre

Hardcover

ISBN 10: 1568814127 ISBN 13: 9781568814124

Publisher: A K Peters/CRC Press, 2007

Synopsis

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 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.

About this title

About the Author

Jean-Pierre Serre

From the Inside Flap

Praise for the first edition of Topics in Galois Theory . . . This 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. Mathematical Reviews

Edition details

• Publisher: A K Peters/CRC Press
• Publication date: 2007
• Language: English
• ISBN 10: 1568814127
• ISBN 13: 9781568814124
• Binding: Hardcover
• Edition number: 2
• Number of pages: 136