Galois Theory Coverings And Riemann Surfaces PDF Download
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Author | : Askold Khovanskii |
Publisher | : Springer Science & Business Media |
Total Pages | : 86 |
Release | : 2013-09-11 |
Genre | : Mathematics |
ISBN | : 3642388418 |
Download Galois Theory, Coverings, and Riemann Surfaces Book in PDF, ePub and Kindle
The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and the classification of coverings over a topological space. The third part contains a geometric description of finite algebraic extensions of the field of meromorphic functions on a Riemann surface and provides an introduction to the topological Galois theory developed by the author. All results are presented in the same elementary and self-contained manner as classical Galois theory, making this book both useful and interesting to readers with a variety of backgrounds in mathematics, from advanced undergraduate students to researchers.
Author | : Askold Khovanskii |
Publisher | : |
Total Pages | : 92 |
Release | : 2013-09-30 |
Genre | : |
ISBN | : 9783642388422 |
Download Galois Theory, Coverings, and Riemann Surfaces Book in PDF, ePub and Kindle
Author | : Matthias Himmelmann |
Publisher | : GRIN Verlag |
Total Pages | : 40 |
Release | : 2018-10-17 |
Genre | : Mathematics |
ISBN | : 3668818967 |
Download Galois Groups and Fundamental Groups on Riemann Surfaces Book in PDF, ePub and Kindle
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 | : Robert D.M. Accola |
Publisher | : Springer |
Total Pages | : 117 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540490566 |
Download Topics in the Theory of Riemann Surfaces Book in PDF, ePub and Kindle
The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus. In addition, the extent to which fixed points of automorphisms are generalized Weierstrass points is considered. The extremely useful inequality of Castelnuovo- Severi is also treated. While the methods are elementary, much of the material does not appear in the current texts on Riemann surfaces, algebraic curves. The book is accessible to a reader who has had an introductory course on the theory of Riemann surfaces or algebraic curves.
Author | : Régine Douady |
Publisher | : Springer Nature |
Total Pages | : 462 |
Release | : 2020-07-13 |
Genre | : Mathematics |
ISBN | : 3030327965 |
Download Algebra and Galois Theories Book in PDF, ePub and Kindle
Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings. This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.
Author | : Tamás Szamuely |
Publisher | : Cambridge University Press |
Total Pages | : 281 |
Release | : 2009-07-16 |
Genre | : Mathematics |
ISBN | : 0521888506 |
Download Galois Groups and Fundamental Groups Book in PDF, ePub and Kindle
Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Author | : Jean-Pierre Serre |
Publisher | : CRC Press |
Total Pages | : 120 |
Release | : 2016-04-19 |
Genre | : Mathematics |
ISBN | : 1439865256 |
Download Topics in Galois Theory Book in PDF, ePub and Kindle
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
Author | : Renzo Cavalieri |
Publisher | : Cambridge University Press |
Total Pages | : 197 |
Release | : 2016-09-26 |
Genre | : Mathematics |
ISBN | : 1316798933 |
Download Riemann Surfaces and Algebraic Curves Book in PDF, ePub and Kindle
Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.
Author | : Helmut Völklein |
Publisher | : Cambridge University Press |
Total Pages | : 270 |
Release | : 1996-08-13 |
Genre | : Mathematics |
ISBN | : 9780521562805 |
Download Groups as Galois Groups Book in PDF, ePub and Kindle
Develops the mathematical background and recent results on the Inverse Galois Problem.
Author | : Frank Neumann |
Publisher | : Springer |
Total Pages | : 240 |
Release | : 2021-09-28 |
Genre | : Mathematics |
ISBN | : 9783030517977 |
Download Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants Book in PDF, ePub and Kindle
This book presents original peer-reviewed contributions from the London Mathematical Society (LMS) Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmüller Theory and Dessinsd'Enfants', which took place at the University of Leicester, UK, from 4 to 7 June, 2018. Within the theme of the workshop, the collected articles cover a broad range of topics and explore exciting new links between algebraic geometry, representation theory, group theory, number theory and algebraic topology. The book combines research and overview articles by prominent international researchers and provides a valuable resource for researchers and students alike.