Galois Theory, Coverings, and Riemann Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Galois Theory, Coverings, and Riemann Surfaces write by Askold Khovanskii. This book was released on 2013-09-11. Galois Theory, Coverings, and Riemann Surfaces available 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.
Galois Theory, Coverings, and Riemann Surfaces
Galois Theory, Coverings, and Riemann Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Galois Theory, Coverings, and Riemann Surfaces write by Askold Khovanskii. This book was released on 2013-09-30. Galois Theory, Coverings, and Riemann Surfaces available in PDF, EPUB and Kindle.
Galois Groups and Fundamental Groups on Riemann Surfaces
Galois Groups and Fundamental Groups on Riemann Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Galois Groups and Fundamental Groups on Riemann Surfaces write by Matthias Himmelmann. This book was released on 2018-10-17. Galois Groups and Fundamental Groups on Riemann Surfaces available 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.
Topics in the Theory of Riemann Surfaces
Topics in the Theory of Riemann Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topics in the Theory of Riemann Surfaces write by Robert D.M. Accola. This book was released on 2006-11-14. Topics in the Theory of Riemann Surfaces available 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.
Algebra and Galois Theories
Algebra and Galois Theories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebra and Galois Theories write by Régine Douady. This book was released on 2020-07-13. Algebra and Galois Theories available 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.
