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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Nanyang Technological University
2022
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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 |
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Science::Mathematics Loh, Colin Jia Sheng Infinite Galois theory and profinite groups |
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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 |
_version_ |
1759854222076018688 |