Topics in Galois theory
著者
書誌事項
Topics in Galois theory
（Research notes in mathematics, v. 1）
A K Peters, c2007
2nd ed
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注記
"Based on 'Topics in Galois theory,' a course given by J-P. Serre at Harvard University in the Fall semester of 1988 and written down by H. Darmon."--Foreword
"For the second edition of these notes, some corrections have been made, and the references have been updated."--Foreword
First ed. published in 1992 by Jones and Bartlett Publishers
Includes bibliographical references (p. 109-117) and index
内容説明・目次
内容説明
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.
目次
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
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