Galois Groups And Fundamental Groups On Riemann Surfaces PDF Download
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Author | : Matthias Himmelmann |
Publisher | : GRIN Verlag |
Total Pages | : 40 |
Release | : 2018-10-17 |
Genre | : Mathematics |
ISBN | : 3668818967 |
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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 | : Leila Schneps |
Publisher | : Cambridge University Press |
Total Pages | : 486 |
Release | : 2003-07-21 |
Genre | : Mathematics |
ISBN | : 9780521808316 |
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Table of contents
Author | : Tamás Szamuely |
Publisher | : Cambridge University Press |
Total Pages | : 281 |
Release | : 2009-07-16 |
Genre | : Mathematics |
ISBN | : 0521888506 |
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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 |
Total Pages | : 281 |
Release | : 2009-07-16 |
Genre | : Mathematics |
ISBN | : 1139481142 |
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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 | : 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 | : 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 | : Otto Forster |
Publisher | : Springer Science & Business Media |
Total Pages | : 262 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461259614 |
Download Lectures on Riemann Surfaces Book in PDF, ePub and Kindle
This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Münster. It provides a concise modern introduction to this rewarding subject, as well as presenting methods used in the study of complex manifolds in the special case of complex dimension one. From the reviews: "This book deserves very serious consideration as a text for anyone contemplating giving a course on Riemann surfaces."—-MATHEMATICAL REVIEWS
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 | : William Mark Goldman |
Publisher | : |
Total Pages | : 69 |
Release | : 2008 |
Genre | : Geometry, Algebraic |
ISBN | : 9781470405106 |
Download Rank One Higgs Bundles and Representations of Fundamental Groups of Riemann Surfaces Book in PDF, ePub and Kindle
Details the theory of rank one Higgs bundles over a closed Riemann surface $X$ and their relation to representations of the fundamental group of $X$. This work constructs an equivalence between the deformation theories of flat connections and Higgs pairs, providing an identification of moduli spaces arising in different contexts.
Author | : Gunter Malle |
Publisher | : Springer Science & Business Media |
Total Pages | : 450 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 3662121239 |
Download Inverse Galois Theory Book in PDF, ePub and Kindle
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.