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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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 |
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DRNTU::Science::Mathematics::Number theory Ma, Liming On automorphism groups of global function fields |
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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. |
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Xing Chaoping |
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Xing Chaoping Ma, Liming |
format |
Theses and Dissertations |
author |
Ma, Liming |
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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 |
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2014 |
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http://hdl.handle.net/10356/55282 |
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1759855116172656640 |