On the Manin–Mumford and Mordell–Lang conjectures in positive characteristic
We prove that in positive characteristic, the Manin–Mumford conjecture implies the Mordell–Lang conjecture in the situation where the ambient variety is an abelian variety defined over the function field of a smooth curve over a finite field and the relevant group is a finitely generated group. In p...
| Autore principale: | |
|---|---|
| Natura: | Journal article |
| Pubblicazione: |
Mathematical Sciences Publishers
2013
|
| _version_ | 1826302974063804416 |
|---|---|
| author | Rössler, D |
| author_facet | Rössler, D |
| author_sort | Rössler, D |
| collection | OXFORD |
| description | We prove that in positive characteristic, the Manin–Mumford conjecture implies the Mordell–Lang conjecture in the situation where the ambient variety is an abelian variety defined over the function field of a smooth curve over a finite field and the relevant group is a finitely generated group. In particular, in the setting of the last sentence, we provide a proof of the Mordell–Lang conjecture that does not depend on tools coming from model theory. |
| first_indexed | 2024-03-07T05:55:35Z |
| format | Journal article |
| id | oxford-uuid:ea616480-b5db-4dea-a73e-5a1446a9c86f |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:55:35Z |
| publishDate | 2013 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | oxford-uuid:ea616480-b5db-4dea-a73e-5a1446a9c86f2022-03-27T11:01:50ZOn the Manin–Mumford and Mordell–Lang conjectures in positive characteristicJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ea616480-b5db-4dea-a73e-5a1446a9c86fSymplectic Elements at OxfordMathematical Sciences Publishers2013Rössler, DWe prove that in positive characteristic, the Manin–Mumford conjecture implies the Mordell–Lang conjecture in the situation where the ambient variety is an abelian variety defined over the function field of a smooth curve over a finite field and the relevant group is a finitely generated group. In particular, in the setting of the last sentence, we provide a proof of the Mordell–Lang conjecture that does not depend on tools coming from model theory. |
| spellingShingle | Rössler, D On the Manin–Mumford and Mordell–Lang conjectures in positive characteristic |
| title | On the Manin–Mumford and Mordell–Lang conjectures in positive characteristic |
| title_full | On the Manin–Mumford and Mordell–Lang conjectures in positive characteristic |
| title_fullStr | On the Manin–Mumford and Mordell–Lang conjectures in positive characteristic |
| title_full_unstemmed | On the Manin–Mumford and Mordell–Lang conjectures in positive characteristic |
| title_short | On the Manin–Mumford and Mordell–Lang conjectures in positive characteristic |
| title_sort | on the manin mumford and mordell lang conjectures in positive characteristic |
| work_keys_str_mv | AT rosslerd onthemaninmumfordandmordelllangconjecturesinpositivecharacteristic |