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.
Galois Groups and Fundamental Groups
Galois Groups and Fundamental Groups - 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 write by Tamás Szamuely. This book was released on 2009-07-16. Galois Groups and Fundamental Groups available in PDF, EPUB and Kindle. 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.
Galois Groups and Fundamental Groups
Galois Groups and Fundamental Groups - 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 write by Leila Schneps. This book was released on 2003-07-21. Galois Groups and Fundamental Groups available in PDF, EPUB and Kindle. Table of contents
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 2013-09-11. 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.
Groups as Galois Groups
Groups as Galois Groups - 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 Groups as Galois Groups write by Helmut Völklein. This book was released on 1996-08-13. Groups as Galois Groups available in PDF, EPUB and Kindle. Develops the mathematical background and recent results on the Inverse Galois Problem.
