The Hasse principle and the Brauer-Manin obstruction for curves
We discuss a range of ways, extending existing methods, to demonstrate violations of the Hasse principle on curves. Of particular interest are curves which contain a rational divisor class of degree 1, even though they contain no rational point. For such curves we construct new types of examples of...
| প্রধান লেখক: | |
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| বিন্যাস: | Journal article |
| প্রকাশিত: |
2004
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| _version_ | 1826306402616868864 |
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| author | Flynn, E |
| author_facet | Flynn, E |
| author_sort | Flynn, E |
| collection | OXFORD |
| description | We discuss a range of ways, extending existing methods, to demonstrate violations of the Hasse principle on curves. Of particular interest are curves which contain a rational divisor class of degree 1, even though they contain no rational point. For such curves we construct new types of examples of violations of the Hasse principle which are due to the Brauer-Manin obstruction, subject to the conjecture that the Tate-Shafarevich group of the Jacobian is finite. |
| first_indexed | 2024-03-07T06:47:26Z |
| format | Journal article |
| id | oxford-uuid:fb56749d-d608-4b0d-a57c-7ad877cbe0cb |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:47:26Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:fb56749d-d608-4b0d-a57c-7ad877cbe0cb2022-03-27T13:12:58ZThe Hasse principle and the Brauer-Manin obstruction for curvesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fb56749d-d608-4b0d-a57c-7ad877cbe0cbMathematical Institute - ePrints2004Flynn, EWe discuss a range of ways, extending existing methods, to demonstrate violations of the Hasse principle on curves. Of particular interest are curves which contain a rational divisor class of degree 1, even though they contain no rational point. For such curves we construct new types of examples of violations of the Hasse principle which are due to the Brauer-Manin obstruction, subject to the conjecture that the Tate-Shafarevich group of the Jacobian is finite. |
| spellingShingle | Flynn, E The Hasse principle and the Brauer-Manin obstruction for curves |
| title | The Hasse principle and the Brauer-Manin obstruction for curves |
| title_full | The Hasse principle and the Brauer-Manin obstruction for curves |
| title_fullStr | The Hasse principle and the Brauer-Manin obstruction for curves |
| title_full_unstemmed | The Hasse principle and the Brauer-Manin obstruction for curves |
| title_short | The Hasse principle and the Brauer-Manin obstruction for curves |
| title_sort | hasse principle and the brauer manin obstruction for curves |
| work_keys_str_mv | AT flynne thehasseprincipleandthebrauermaninobstructionforcurves AT flynne hasseprincipleandthebrauermaninobstructionforcurves |