Two-dimensional local-global class field theory in positive characteristic
Using the higher tame symbol and Kawada and Satake’s Witt vector method, A.N. Parshin developed class field theory for positive characteristic higher local fields, defining reciprocity maps separately for the tamely ramified and wildly ramified cases. We prove reciprocity laws for these symbols usin...
| Main Author: | |
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2014
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| Online Access: | https://eprints.nottingham.ac.uk/14538/ |
| _version_ | 1848791985141317632 |
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| author | Syder, Kirsty |
| author_facet | Syder, Kirsty |
| author_sort | Syder, Kirsty |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Using the higher tame symbol and Kawada and Satake’s Witt vector method, A.N. Parshin developed class field theory for positive characteristic higher local fields, defining reciprocity maps separately for the tamely ramified and wildly ramified cases. We prove reciprocity laws for these symbols using techniques of Morrow for the Witt symbol and Romo for the higher tame symbol. We then extend this method of defining a reciprocity map to the case of positive characteristic local- global fields associated to points and curves on an algebraic surface over a finite field. |
| first_indexed | 2025-11-14T18:37:12Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-14538 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:37:12Z |
| publishDate | 2014 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-145382025-02-28T11:31:30Z https://eprints.nottingham.ac.uk/14538/ Two-dimensional local-global class field theory in positive characteristic Syder, Kirsty Using the higher tame symbol and Kawada and Satake’s Witt vector method, A.N. Parshin developed class field theory for positive characteristic higher local fields, defining reciprocity maps separately for the tamely ramified and wildly ramified cases. We prove reciprocity laws for these symbols using techniques of Morrow for the Witt symbol and Romo for the higher tame symbol. We then extend this method of defining a reciprocity map to the case of positive characteristic local- global fields associated to points and curves on an algebraic surface over a finite field. 2014-12-09 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/14538/1/Thesis.pdf Syder, Kirsty (2014) Two-dimensional local-global class field theory in positive characteristic. PhD thesis, University of Nottingham. |
| spellingShingle | Syder, Kirsty Two-dimensional local-global class field theory in positive characteristic |
| title | Two-dimensional local-global class field theory in positive characteristic |
| title_full | Two-dimensional local-global class field theory in positive characteristic |
| title_fullStr | Two-dimensional local-global class field theory in positive characteristic |
| title_full_unstemmed | Two-dimensional local-global class field theory in positive characteristic |
| title_short | Two-dimensional local-global class field theory in positive characteristic |
| title_sort | two-dimensional local-global class field theory in positive characteristic |
| url | https://eprints.nottingham.ac.uk/14538/ |