Topics in Galois Theory: Research Notes in Mathematics

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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.

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

Jean-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.