On automorphism groups of global function fields

In this thesis, we first give a characterization of fixed fields under subgroups of the decomposition group $\mathcal{A}(P_\infty)$ of the Deligne--Lusztig function fields. More specifically, we give a characterization of subgroups in the decomposition group by means of a necessary and sufficient c...

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Main Author: Ma, Liming
Other Authors: Xing Chaoping
Format: Theses and Dissertations
Language:English
Published: 2014
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Online Access:http://hdl.handle.net/10356/55282
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-552822023-02-28T23:42:27Z On automorphism groups of global function fields Ma, Liming Xing Chaoping School of Physical and Mathematical Sciences Yeo Sze Ling DRNTU::Science::Mathematics::Number theory In this thesis, we first give a characterization of fixed fields under subgroups of the decomposition group $\mathcal{A}(P_\infty)$ of the Deligne--Lusztig function fields. More specifically, we give a characterization of subgroups in the decomposition group by means of a necessary and sufficient condition. By establishing an analogue of Kneser's theorem on the Hermitian product over vector spaces, we determine the genera set consisting of all the genera of fixed fields of subgroups of the decomposition group for the Hermitian function field with an odd characteristic. In addition, we also improve the results for other cases of the Deligne--Lusztig function fields. In the second part, we concentrate on determining the automorphism groups of cyclotomic function fields with modulus $x^{n+1}$ and $P$ over the rational function fields, where $n\ge 1$ and $P$ is an irreducible polynomial of degree two. We also investigate the automorphism groups of some subfields of cyclotomic function fields. ​Doctor of Philosophy (SPMS) 2014-01-07T09:06:59Z 2014-01-07T09:06:59Z 2013 2013 Thesis Ma, L. (2013). On automorphism groups of global function fields. Doctoral thesis, Nanyang Technological University, Singapore. http://hdl.handle.net/10356/55282 en 141 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Mathematics::Number theory
spellingShingle DRNTU::Science::Mathematics::Number theory
Ma, Liming
On automorphism groups of global function fields
description In this thesis, we first give a characterization of fixed fields under subgroups of the decomposition group $\mathcal{A}(P_\infty)$ of the Deligne--Lusztig function fields. More specifically, we give a characterization of subgroups in the decomposition group by means of a necessary and sufficient condition. By establishing an analogue of Kneser's theorem on the Hermitian product over vector spaces, we determine the genera set consisting of all the genera of fixed fields of subgroups of the decomposition group for the Hermitian function field with an odd characteristic. In addition, we also improve the results for other cases of the Deligne--Lusztig function fields. In the second part, we concentrate on determining the automorphism groups of cyclotomic function fields with modulus $x^{n+1}$ and $P$ over the rational function fields, where $n\ge 1$ and $P$ is an irreducible polynomial of degree two. We also investigate the automorphism groups of some subfields of cyclotomic function fields.
author2 Xing Chaoping
author_facet Xing Chaoping
Ma, Liming
format Theses and Dissertations
author Ma, Liming
author_sort Ma, Liming
title On automorphism groups of global function fields
title_short On automorphism groups of global function fields
title_full On automorphism groups of global function fields
title_fullStr On automorphism groups of global function fields
title_full_unstemmed On automorphism groups of global function fields
title_sort on automorphism groups of global function fields
publishDate 2014
url http://hdl.handle.net/10356/55282
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