Für diesen Artikel ist leider kein Bild verfügbar.

Galois Groups and Fundamental Groups on Riemann Surfaces

Matthias Himmelmann (Autor)

Buch | Softcover

48 Seiten

2018 | 18001 A. 1. Auflage
GRIN Verlag
978-3-668-81897-2 (ISBN)

Titel nicht im Sortiment

Artikel merken

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.

Erscheinungsdatum	26.10.2018
Sprache	englisch
Maße	148 x 210 mm
Gewicht	83 g
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Algebra • Algebraic • algebraische • categories • completion • Cone • coverings • Finite étale • Finiteétale • Fläche • Functions • fundamental • Fundamentalgruppe • Galois • Geometrie • Geometry • Group • Gruppe • Gruppentheorie • Hawaiian earring • Hawaiianearring • Hawaiischer Ohrring • HawaiischerOhrring • Kategorien • Meromorph • Meromorphic • Profinit • Profinite • Riemann • Riemannsche • Szamuely • Topologie • Topology • Überdeckung • Überdeckungen • Universal • Vervollständigung
ISBN-10	3-668-81897-5 / 3668818975
ISBN-13	978-3-668-81897-2 / 9783668818972
Zustand	Neuware