Galois Groups and Fundamental Groups on Riemann Surfaces is popular PDF and ePub book, written by Matthias Himmelmann in 2018-10-17, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Galois Groups and Fundamental Groups on Riemann Surfaces can be Read Online from any device for your convenience.
Galois Groups and Fundamental Groups on Riemann Surfaces Book PDF Summary
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.
Detail Book of Galois Groups and Fundamental Groups on Riemann Surfaces PDF
- Author : Matthias Himmelmann
- Release : 17 October 2018
- Publisher : GRIN Verlag
- ISBN : 9783668818965
- Genre : Mathematics
- Total Page : 46 pages
- Language : English
- PDF File Size : 10,9 Mb
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