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 existen...
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| Այլ հեղինակներ: | |
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Springer
2004
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| _version_ | 1826273720991219712 |
|---|---|
| author | Bruin, N Flynn, E |
| author2 | Buell, D |
| author_facet | Buell, D 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 | 2024-03-06T22:32:31Z |
| format | Conference item |
| id | oxford-uuid:58bdc51b-d1f4-41a4-9b87-c5a2c8029ca8 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:32:31Z |
| publishDate | 2004 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:58bdc51b-d1f4-41a4-9b87-c5a2c8029ca82022-03-26T17:05:32ZRational Divisors in Rational Divisor Classes.Conference itemhttp://purl.org/coar/resource_type/c_5794uuid:58bdc51b-d1f4-41a4-9b87-c5a2c8029ca8Symplectic Elements at OxfordSpringer2004Bruin, NFlynn, EBuell, DWe 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 |