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Author: Tamás Szamuely
Publisher: Cambridge University Press
ISBN: 0521888506
Category : Mathematics
Languages : en
Pages : 281
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Book Description
Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Author: Tamás Szamuely
Publisher: Cambridge University Press
ISBN: 0521888506
Category : Mathematics
Languages : en
Pages : 281
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Book Description
Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Author: Tamás Szamuely
Publisher: Cambridge University Press
ISBN: 1139481142
Category : Mathematics
Languages : en
Pages : 281
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Book Description
Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful interplay between algebra and topology that underpins much modern research in geometry and number theory. Assuming as little technical background as possible, the book starts with basic algebraic and topological concepts, but already presented from the modern viewpoint advocated by Grothendieck. This enables a systematic yet accessible development of the theories of fundamental groups of algebraic curves, fundamental groups of schemes, and Tannakian fundamental groups. The connection between fundamental groups and linear differential equations is also developed at increasing levels of generality. Key applications and recent results, for example on the inverse Galois problem, are given throughout.
Author: Leila Schneps
Publisher: Cambridge University Press
ISBN: 9780521808316
Category : Mathematics
Languages : en
Pages : 486
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Book Description
Table of contents
Author: Y. Ihara
Publisher: Springer Science & Business Media
ISBN: 1461396492
Category : Mathematics
Languages : en
Pages : 454
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Book Description
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.
Author: Helmut Völklein
Publisher: Cambridge University Press
ISBN: 9780521562805
Category : Mathematics
Languages : en
Pages : 270
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Book Description
Develops the mathematical background and recent results on the Inverse Galois Problem.
Author: Matthias Himmelmann
Publisher: GRIN Verlag
ISBN: 3668818967
Category : Mathematics
Languages : en
Pages : 40
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Book Description
Bachelor Thesis from the year 2018 in the subject Mathematics - Algebra, grade: 1,0, Free University of Berlin (Mathematik), language: English, abstract: This thesis deals with the correlation of the fundamental group and the Galois group, using their corresponding entities of covering spaces and field extensions. First it is viewed in the general setting of categories, using the language of Galois categories. It is shown that the categories of the finite étale algebras and the category of covering spaces are correlated, which gives the fact that the profinite completion of the fundamental group and the absolute Galois group are similar. More specifically, on Riemann surfaces it is shown that there exists an anti-equivalence of categories between the finite field extensions of the meromorphic functions of a compact, connected Riemann Surface X and the category of branched coverings of X. A more explicit theorem, that provides an isomorphism between a specific Galois Group and the profinite Completion of the Fundamental Group of a pointed X, gives more insight on the behaviour of these two groups.
Author: John Coates
Publisher: Cambridge University Press
ISBN: 1139505653
Category : Mathematics
Languages : en
Pages : 321
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Book Description
This book describes the interaction between several key aspects of Galois theory based on Iwasawa theory, fundamental groups and automorphic forms. These ideas encompass a large portion of mainstream number theory and ramifications that are of interest to graduate students and researchers in number theory, algebraic geometry, topology and physics.
Author: Gunter Malle
Publisher: Springer Science & Business Media
ISBN: 3662121239
Category : Mathematics
Languages : en
Pages : 450
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Book Description
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.
Author: Michio Kuga
Publisher: Springer Science & Business Media
ISBN: 1461203295
Category : Mathematics
Languages : en
Pages : 147
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Book Description
First year, undergraduate, mathematics students in Japan have for many years had the opportunity of a unique experience---an introduction, at an elementary level, to some very advanced ideas in mathematics from one of the leading mathematicians of the world. English reading students now have the opportunity to enjoy this lively presentation, from elementary ideas to cartoons to funny examples, and to follow the mind of an imaginative and creative mathematician into a world of enduring mathematical creations.
Author: Jean-Pierre Serre
Publisher: CRC Press
ISBN: 1439865256
Category : Mathematics
Languages : en
Pages : 120
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Book Description
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 constructi
