Journal article
On the Manin–Mumford and Mordell–Lang conjectures in positive characteristic
- Abstract:
- 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 993.2KB, Terms of use)
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- Publisher copy:
- 10.2140/ant.2013.7.2039
Authors
- Publisher:
- Mathematical Sciences Publishers
- Journal:
- Algebra and Number Theory More from this journal
- Volume:
- 7
- Issue:
- 8
- Pages:
- 2039-2057
- Publication date:
- 2013-11-24
- Acceptance date:
- 2012-11-23
- DOI:
- EISSN:
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1944-7833
- ISSN:
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1937-0652
- Keywords:
- Pubs id:
-
pubs:745036
- UUID:
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uuid:ea616480-b5db-4dea-a73e-5a1446a9c86f
- Local pid:
-
pubs:745036
- Source identifiers:
-
745036
- Deposit date:
-
2018-05-05
Terms of use
- Copyright holder:
- Mathematical Sciences Publishers
- Copyright date:
- 2013
- Notes:
- © 2013 Mathematical Sciences Publishers.
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