Rational divisors in rational divisor classes
We discuss the situation where a curve C, defined over a number field K, has a known K-rational divisor class of degree 1, and consider whether this class contains an actual K-rational divisor. When C has points everywhere locally, the local to global principle of the Brauer group gives the existenc...
| Main Authors: | , |
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| Format: | Book section |
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Springer
2004
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| _version_ | 1797097660246654976 |
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| author | Bruin, N Flynn, E |
| author_facet | Bruin, N Flynn, E |
| author_sort | Bruin, N |
| collection | OXFORD |
| description | We discuss the situation where a curve C, defined over a number field K, has a known K-rational divisor class of degree 1, and consider whether this class contains an actual K-rational divisor. When C has points everywhere locally, the local to global principle of the Brauer group gives the existence of such a divisor. In this situation, we give an alternative, more down to earth, approach, which indicates how to compute this divisor in certain situations. We also discuss examples where C does not have points everywhere locally, and where no such K-rational divisor is contained in the K-rational divisor class. |
| first_indexed | 2024-03-07T04:58:39Z |
| format | Book section |
| id | oxford-uuid:d77e06a9-1366-4966-8e5c-caa404d8673f |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:58:39Z |
| publishDate | 2004 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:d77e06a9-1366-4966-8e5c-caa404d8673f2022-03-27T08:41:27ZRational divisors in rational divisor classesBook sectionhttp://purl.org/coar/resource_type/c_3248uuid:d77e06a9-1366-4966-8e5c-caa404d8673fMathematical Institute - ePrintsSpringer2004Bruin, NFlynn, EWe discuss the situation where a curve C, defined over a number field K, has a known K-rational divisor class of degree 1, and consider whether this class contains an actual K-rational divisor. When C has points everywhere locally, the local to global principle of the Brauer group gives the existence of such a divisor. In this situation, we give an alternative, more down to earth, approach, which indicates how to compute this divisor in certain situations. We also discuss examples where C does not have points everywhere locally, and where no such K-rational divisor is contained in the K-rational divisor class. |
| spellingShingle | Bruin, N Flynn, E Rational divisors in rational divisor classes |
| title | Rational divisors in rational divisor classes |
| title_full | Rational divisors in rational divisor classes |
| title_fullStr | Rational divisors in rational divisor classes |
| title_full_unstemmed | Rational divisors in rational divisor classes |
| title_short | Rational divisors in rational divisor classes |
| title_sort | rational divisors in rational divisor classes |
| work_keys_str_mv | AT bruinn rationaldivisorsinrationaldivisorclasses AT flynne rationaldivisorsinrationaldivisorclasses |