Galois Groups Over
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Galois Groups Over
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Author : Y. Ihara
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Galois Groups Over written by Y. Ihara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume is the offspring of a week-long workshop on "Galois groups over Q and related topics," which was held at the Mathematical Sciences Research Institute during the week March 23-27, 1987. The organizing committee consisted of Kenneth Ribet (chairman), Yasutaka Ihara, and Jean-Pierre Serre. The conference focused on three principal themes: 1. Extensions of Q with finite simple Galois groups. 2. Galois actions on fundamental groups, nilpotent extensions of Q arising from Fermat curves, and the interplay between Gauss sums and cyclotomic units. 3. Representations of Gal(Q/Q) with values in GL(2)j deformations and connections with modular forms. Here is a summary of the conference program: • G. Anderson: "Gauss sums, circular units and the simplex" • G. Anderson and Y. Ihara: "Galois actions on 11"1 ( ••• ) and higher circular units" • D. Blasius: "Maass forms and Galois representations" • P. Deligne: "Galois action on 1I"1(P-{0, 1, oo}) and Hodge analogue" • W. Feit: "Some Galois groups over number fields" • Y. Ihara: "Arithmetic aspect of Galois actions on 1I"1(P - {O, 1, oo})" - survey talk • U. Jannsen: "Galois cohomology of i-adic representations" • B. Matzat: - "Rationality criteria for Galois extensions" - "How to construct polynomials with Galois group Mll over Q" • B. Mazur: "Deforming GL(2) Galois representations" • K. Ribet: "Lowering the level of modular representations of Gal( Q/ Q)" • J-P. Serre: - Introductory Lecture - "Degree 2 modular representations of Gal(Q/Q)" • J.
Groups As Galois Groups
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Author : Helmut Völklein
language : en
Publisher: Cambridge University Press
Release Date : 1996-08-13
Groups As Galois Groups written by Helmut Völklein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-13 with Mathematics categories.
Develops the mathematical background and recent results on the Inverse Galois Problem.
Galois Groups And Fundamental Groups
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Author : Tamás Szamuely
language : en
Publisher: Cambridge University Press
Release Date : 2009-07-16
Galois Groups And Fundamental Groups written by Tamás Szamuely and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-16 with Mathematics categories.
Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
The Absolute Galois Group Of A Semi Local Field
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Author : Dan Haran
language : en
Publisher: Springer Nature
Release Date : 2021-11-19
The Absolute Galois Group Of A Semi Local Field written by Dan Haran and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-19 with Mathematics categories.
This book is devoted to the structure of the absolute Galois groups of certain algebraic extensions of the field of rational numbers. Its main result, a theorem proved by the authors and Florian Pop in 2012, describes the absolute Galois group of distinguished semi-local algebraic (and other) extensions of the rational numbers as free products of the free profinite group on countably many generators and local Galois groups. This is an instance of a positive answer to the generalized inverse problem of Galois theory. Adopting both an arithmetic and probabilistic approach, the book carefully sets out the preliminary material needed to prove the main theorem and its supporting results. In addition, it includes a description of Melnikov's construction of free products of profinite groups and, for the first time in book form, an account of a generalization of the theory of free products of profinite groups and their subgroups. The book will be of interest to researchers in field arithmetic, Galois theory and profinite groups.
Inverse Galois Theory
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Author : Gunter Malle
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Inverse Galois Theory written by Gunter Malle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
A consistent and near complete survey of the important progress made in the field over the last few years, with the main emphasis on the rigidity method and its applications. Among others, this monograph presents the most successful existence theorems known and construction methods for Galois extensions as well as solutions for embedding problems combined with a collection of the existing Galois realizations.
Realizing Certain Groups As Galois Groups Over The Rationals
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Author : Robert Louis Chaput
language : en
Publisher:
Release Date : 1975
Realizing Certain Groups As Galois Groups Over The Rationals written by Robert Louis Chaput and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Galois theory categories.
Galois Groups Over Q
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Author : Yasutaka Ihara
language : en
Publisher:
Release Date : 1989-01-01
Galois Groups Over Q written by Yasutaka Ihara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Galois theory categories.
Galois Theory Through Exercises
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Author : Juliusz Brzeziński
language : en
Publisher: Springer
Release Date : 2018-03-21
Galois Theory Through Exercises written by Juliusz Brzeziński and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-21 with Mathematics categories.
This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.
Galois Theory Of P Extensions
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Author : Helmut Koch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Galois Theory Of P Extensions written by Helmut Koch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Helmut Koch's classic is now available in English. Competently translated by Franz Lemmermeyer, it introduces the theory of pro-p groups and their cohomology. The book contains a postscript on the recent development of the field written by H. Koch and F. Lemmermeyer, along with many additional recent references.
Galois Groups And Fundamental Groups
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Author : Leila Schneps
language : en
Publisher: Cambridge University Press
Release Date : 2003-07-21
Galois Groups And Fundamental Groups written by Leila Schneps and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-21 with Mathematics categories.
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