Galois Groups and Fundamental Groups (Cambridge Studies in Advanced Mathematics)
| Author | : | |
| Rating | : | 4.91 (642 Votes) |
| Asin | : | 0521888506 |
| Format Type | : | paperback |
| Number of Pages | : | 282 Pages |
| Publish Date | : | 2017-01-11 |
| Language | : | English |
DESCRIPTION:
Tamás Szamuely is a Senior Research Fellow in the Alfréd Rényi Institute of Mathematics at the Hungarian Academy of Sciences, Budapest.
On the whole, the book is useful for mathematicians and graduate students looking for one place where they can find information about the etale fundamental group and the related Nori fundamental group scheme." Swaminathan Subramanian, Mathematical Reviews . "The book is well written and contains much information about the etale fundamental group. There are exercises in every chapter
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. 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. 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. Key applications and recent results, for example on the inverse Galois problem, are given throughout.. The connection between fundamental groups and linear differential equations is also developed at increasing levels of generality. This enables a systematic yet accessible development of the theories of fundamental groups of algebraic curves, fundamental groups of schemes, and Tannakian fundamental groups
Pleasant read. This book answered a lot of my needs- the coverage on the fundamental groups of schemes made my senior thesis a lot better- the exposition helped my understand the ideas clearly, which translated to my writing. I recommend this to any mathematician looking for a fun book (we do have a characteristic definition of fun). I appreciate the authors writing style- it does not have pretentious/know-it-all tone.. A masterfully written guide to a rich and deep theory Pat "Everyone" who has taken a course covering Galois Theory of Fields and a course covering Fundamental Groups of Topological Spaces (that is to say, strong undergraduate students and beginning graduate students in mathematics) recognizes that the correspondence between Galois extensions and subgroups of the absolute Galois group is "the same thing" as the correspondence between covering spaces and subgroups of the fundamental group. T