Galois Theory, Coverings, and Riemann Surfaces
Contents:
Could anybody please enlighten me a bit as to what this is saying?
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It sounds really interesting and I would love to learn more about this overlap , but I'm not too sure exactly where to start. It would be nice to have an answer with a brief overview in it, and not just some sources, since I'm really meant to be revising for exams, so don't have masses of time at the moment to explore the bits of maths that I would like to!
The following three categories are equivalent:. Some of the functors between these are easy to describe. By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service , privacy policy and cookie policy , and that your continued use of the website is subject to these policies. Home Questions Tags Users Unanswered. Link between Riemann surfaces and Galois theory Ask Question.
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In my notes for a Geometry of Surfaces course that I'm studying, there is the following quote: Tim 1, 1 10 I don't know nearly as much about this as I would like to. And then something like, if the mapping is injective it is a cover, the index tells you the number of ramification points, or something else like this that I don't actually know anything about.
Or, get it for Kobo Super Points! Volume 3, Complex Analysis, Measure and Integration. Group theory and differential equations, Birkhauser. Sign up or log in Sign up using Google. I'm an undergrad who recently started working through this myself. Elements of the Theory of Functions. An Introduction to Fourier Series and Integrals.
There is a really nice brief overview of Riemann surfaces, algebraic curves and the like in Algebraic Geometry I - Riemann Surfaces and Algebraic Curves by Shokurov edited by Shafarevich. And by brief I mean it covers the main points all the way up to this subject in the first thirty pages but all four volumes make up pages The following three categories are equivalent: Compact connected Riemann surfaces and nonconstant holomorphic maps.
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Qiaochu Yuan k 32 The book is basic but beautiful. Group theory and differential equations, Birkhauser.
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He does not cover branched covers though. Complex Algebraic Curves, London Math. I think chapters 4 and 5 are the places where your student should check first, and I think they don't require previous chapters to follow what is there. Also, Inverse Galois theory by Malle and Matzat is great to see some applications of what he is learning is his project--mainly chapter 1.
This one needs more background than the above, so I'm just recommending this one after he has learned the material in the other one. The first sections of the following two papers contain background material on covering spaces and Galois theory. Joe Harris Galois groups of enumerative problems Duke Math. Volume 46, Number 4 , Don't know of anything alike in english, yet. Approaching the problem from a slightly different position, you could point your student towards a Masters' thesis:.
There are some more or small errors, and the aim is slightly different, so the task might then be to rewrite that slightly too SGA1 based perhaps , to check for errors, adapting it towards the aims that you have in mind and bringing in more Riemann surface stuff. By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service , privacy policy and cookie policy , and that your continued use of the website is subject to these policies.
Home Questions Tags Users Unanswered. Good book on Riemann surfaces and Galois theory? Nick Addington 2 Douady if you can read french? McKean and Moll's book Elliptic Curves might be a bit elementary but I like their discussion of this a lot.
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Feb 17 '12 at Douady and Douady is appealing to me, but it's probably too sophisticated for my student - they define the field of meromorphic functions as a projective limit, for example. McKean and Moll is more the right style, although I'm having trouble finding where they address the fact that I asked about.
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. Editorial Reviews. Review. From the reviews: “This book features generalizations and Galois Theory, Coverings, and Riemann Surfaces Edition, Kindle.
Simon Donaldson's new book "Riemann Surfaces" looks very nice if I could scare up a copy Lars 2, 2 23 Thanks, although judging by the table of contents it may be too sheafy for an undergrad. Anyway it seems hard to come by - I can't find it in the library or online. Peter Dalakov 2, 11 I'm an undergrad who recently started working through this myself.
What a lovely book.