A01=Jean-Pierre Serre
Abelian Group
Absolutely Irreducible
algebraic
Algebraic Closure
Algebraic Group
Author_Jean-Pierre Serre
Category=PBF
Category=PBG
class
closure
Commutator Subgroup
conjugacy
Conjugacy Classes
curve
Cyclic Extension
Dense
dihedral
elliptic
Elliptic Curve
Embedding Problem
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
extension
field extension construction
finite group realization
Frattini Subgroup
Fundamental Group ?1
Fundamental Group Π1
Galois Closure
Galois Extension
Galois Group
group
Hilbert irreducibility
inertia
Inertia Group
Linearly Disjoint
Maximal Subgroups
Minimal Polynomial
nilpotent group theory
Projective Algebraic Varieties
Quadratic Extension
Quaternion Algebra
rationality criteria
Regular Extension
regular extensions of rational function fields
rigidity method
Symmetric Group Sn
Unique Conjugacy Class
Product details
- ISBN 9781568814124
- Weight: 317g
- Dimensions: 152 x 229mm
- Publication Date: 02 Nov 2007
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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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.
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.
