Infinite Galois theory and profinite groups

This paper aims to provide an exposition on infinite Galois extensions and profinite groups as well as some applications of Galois theory through six chapters. We will begin with an introduction to topological groups, inverse system and inverse limits of topological spaces and topological groups. Th...

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Main Author: Loh, Colin Jia Sheng
Other Authors: Wu Guohua
Format: Final Year Project
Language:English
Published: Nanyang Technological University 2022
Subjects:
Online Access:https://hdl.handle.net/10356/156819
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1568192023-02-28T23:13:00Z Infinite Galois theory and profinite groups Loh, Colin Jia Sheng Wu Guohua School of Physical and Mathematical Sciences guohua@ntu.edu.sg Science::Mathematics This paper aims to provide an exposition on infinite Galois extensions and profinite groups as well as some applications of Galois theory through six chapters. We will begin with an introduction to topological groups, inverse system and inverse limits of topological spaces and topological groups. Thereafter, we will introduce profinite groups and provide a characterisation of profinite groups as Galois groups by proving Krull’s Theorem on infinite Galois extensions. To end it off, we will explore the norm and trace maps of Galois extension and their applications including the Hilbert’s Theorem 90 and its generalisation in the study of group cohomology. Bachelor of Science in Mathematical Sciences 2022-04-26T06:59:43Z 2022-04-26T06:59:43Z 2022 Final Year Project (FYP) Loh, C. J. S. (2022). Infinite Galois theory and profinite groups. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/156819 https://hdl.handle.net/10356/156819 en application/pdf Nanyang Technological University
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
spellingShingle Science::Mathematics
Loh, Colin Jia Sheng
Infinite Galois theory and profinite groups
description This paper aims to provide an exposition on infinite Galois extensions and profinite groups as well as some applications of Galois theory through six chapters. We will begin with an introduction to topological groups, inverse system and inverse limits of topological spaces and topological groups. Thereafter, we will introduce profinite groups and provide a characterisation of profinite groups as Galois groups by proving Krull’s Theorem on infinite Galois extensions. To end it off, we will explore the norm and trace maps of Galois extension and their applications including the Hilbert’s Theorem 90 and its generalisation in the study of group cohomology.
author2 Wu Guohua
author_facet Wu Guohua
Loh, Colin Jia Sheng
format Final Year Project
author Loh, Colin Jia Sheng
author_sort Loh, Colin Jia Sheng
title Infinite Galois theory and profinite groups
title_short Infinite Galois theory and profinite groups
title_full Infinite Galois theory and profinite groups
title_fullStr Infinite Galois theory and profinite groups
title_full_unstemmed Infinite Galois theory and profinite groups
title_sort infinite galois theory and profinite groups
publisher Nanyang Technological University
publishDate 2022
url https://hdl.handle.net/10356/156819
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