Galois Groups and Fundamental Groups

Nonfiction, Science & Nature, Mathematics, Number Theory, Algebra
Cover of the book Galois Groups and Fundamental Groups by Tamás Szamuely, Cambridge University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Tamás Szamuely ISBN: 9781139637732
Publisher: Cambridge University Press Publication: July 16, 2009
Imprint: Cambridge University Press Language: English
Author: Tamás Szamuely
ISBN: 9781139637732
Publisher: Cambridge University Press
Publication: July 16, 2009
Imprint: Cambridge University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Cambridge University Press

Cover of the book Herder's Hermeneutics by Tamás Szamuely
Cover of the book Big Copyright Versus the People by Tamás Szamuely
Cover of the book Selected Discourses of Shenoute the Great by Tamás Szamuely
Cover of the book FRCR Part 1 Anatomy Mock Examinations by Tamás Szamuely
Cover of the book The Cambridge Companion to the Epic by Tamás Szamuely
Cover of the book Executive Function and Dysfunction by Tamás Szamuely
Cover of the book Accounting for Carbon by Tamás Szamuely
Cover of the book Transparency in International Law by Tamás Szamuely
Cover of the book Origen: Contra Celsum by Tamás Szamuely
Cover of the book Compendium of Sustainable Energy Laws by Tamás Szamuely
Cover of the book Policy and Planning for Endangered Languages by Tamás Szamuely
Cover of the book Discriminant Equations in Diophantine Number Theory by Tamás Szamuely
Cover of the book Institutional Work by Tamás Szamuely
Cover of the book Social Rights Judgments and the Politics of Compliance by Tamás Szamuely
Cover of the book Anesthesia Oral Board Review by Tamás Szamuely
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy