Towards a characterization of subfields of the Deligne–Lusztig function fields
In this paper, we give a characterization of subgroups contained in the decomposition group A(P∞) of a rational place P∞ by means of a necessary and sufficient condition for each of the three types of function fields of Deligne–Lusztig curves. In particular, we translate the problems on the genera o...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
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| Online Access: | https://hdl.handle.net/10356/97707 http://hdl.handle.net/10220/18111 |
| _version_ | 1826113112788434944 |
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| author | Bassa, Alp Ma, Liming Xing, Chaoping Yeo, Sze Ling |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Bassa, Alp Ma, Liming Xing, Chaoping Yeo, Sze Ling |
| author_sort | Bassa, Alp |
| collection | NTU |
| description | In this paper, we give a characterization of subgroups contained in the decomposition group A(P∞) of a rational place P∞ by means of a necessary and sufficient condition for each of the three types of function fields of Deligne–Lusztig curves. In particular, we translate the problems on the genera of subfields of the Deligne–Lusztig function fields to the combinatorial problems concerning some specific vector spaces and their dimensions. This allows us to determine the genera set consisting of all the genera of the fixed fields of subgroups of the decomposition group A(P∞) for the Hermitian function field over Fq where q is a power of an odd prime. Promising results pertaining to the genera of subfields of the other types of Deligne–Lusztig function fields are provided as well. Indeed, it turns out that we improve many previous results given by Garcia–Stichtenoth–Xing, Giulietti–Korchmáros–Torres and Çakçak–Özbudak on the subfields of function fields of Deligne–Lusztig curves. |
| first_indexed | 2024-10-01T03:18:11Z |
| format | Journal Article |
| id | ntu-10356/97707 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:18:11Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/977072020-03-07T12:37:05Z Towards a characterization of subfields of the Deligne–Lusztig function fields Bassa, Alp Ma, Liming Xing, Chaoping Yeo, Sze Ling School of Physical and Mathematical Sciences DRNTU::Science::Mathematics In this paper, we give a characterization of subgroups contained in the decomposition group A(P∞) of a rational place P∞ by means of a necessary and sufficient condition for each of the three types of function fields of Deligne–Lusztig curves. In particular, we translate the problems on the genera of subfields of the Deligne–Lusztig function fields to the combinatorial problems concerning some specific vector spaces and their dimensions. This allows us to determine the genera set consisting of all the genera of the fixed fields of subgroups of the decomposition group A(P∞) for the Hermitian function field over Fq where q is a power of an odd prime. Promising results pertaining to the genera of subfields of the other types of Deligne–Lusztig function fields are provided as well. Indeed, it turns out that we improve many previous results given by Garcia–Stichtenoth–Xing, Giulietti–Korchmáros–Torres and Çakçak–Özbudak on the subfields of function fields of Deligne–Lusztig curves. 2013-12-05T06:47:38Z 2019-12-06T19:45:43Z 2013-12-05T06:47:38Z 2019-12-06T19:45:43Z 2013 2013 Journal Article Bassa, A., Ma, L., Xing, C., & Yeo, S. L. (2013). Towards a characterization of subfields of the Deligne–Lusztig function fields. Journal of combinatorial theory, series A, 120(7), 1351-1371. 0097-3165 https://hdl.handle.net/10356/97707 http://hdl.handle.net/10220/18111 10.1016/j.jcta.2013.04.001 en Journal of combinatorial theory, series A |
| spellingShingle | DRNTU::Science::Mathematics Bassa, Alp Ma, Liming Xing, Chaoping Yeo, Sze Ling Towards a characterization of subfields of the Deligne–Lusztig function fields |
| title | Towards a characterization of subfields of the Deligne–Lusztig function fields |
| title_full | Towards a characterization of subfields of the Deligne–Lusztig function fields |
| title_fullStr | Towards a characterization of subfields of the Deligne–Lusztig function fields |
| title_full_unstemmed | Towards a characterization of subfields of the Deligne–Lusztig function fields |
| title_short | Towards a characterization of subfields of the Deligne–Lusztig function fields |
| title_sort | towards a characterization of subfields of the deligne lusztig function fields |
| topic | DRNTU::Science::Mathematics |
| url | https://hdl.handle.net/10356/97707 http://hdl.handle.net/10220/18111 |
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