Journal article

Rational points in periodic analytic sets and the Manin-Mumford conjecture

Abstract:: We present a new proof of the Manin-Mumford conjecture about torsion points on algebraic subvarieties of abelian varieties. Our principle, which admits other applications, is to view torsion points as rational points on a complex torus and then compare (i) upper bounds for the number of rational points on a transcendental analytic variety (Bombieri-Pila-Wilkie) and (ii) lower bounds for the degree of a torsion point (Masser), after taking conjugates. In order to be able to deal with (i), we discuss (Thm. 2.1) the semi-algebraic curves contained in an analytic variety supposed invariant for translations by a full lattice, which is a topic with some independent motivation.

Publication status:: Published

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APA Style

Pila, J., & Zannier, U. (2008). Rational points in periodic analytic sets and the Manin-Mumford conjecture. RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, 19(2), 149–162.

MLA Style

Pila, J., and U. Zannier. “Rational Points in Periodic Analytic Sets and the Manin-Mumford Conjecture.” RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, vol. 19, no. 2, 2008, pp. 149–62.

Chicago Style

Pila, J, and U Zannier. 2008. “Rational Points in Periodic Analytic Sets and the Manin-Mumford Conjecture.” RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI 19 (2): 149–62.
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Publisher copy:: 10.4171/RLM/514

Authors

+ Pila, J More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Zannier, U More by this author

Role:: Author

Journal:: RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI More from this journal
Volume:: 19
Issue:: 2
Pages:: 149-162
Publication date:: 2008-02-27
DOI:: 10.4171/RLM/514
EISSN:: 1720-0768
ISSN:: 1120-6330

Language:: English
Keywords:: math.NT

math.AG
Pubs id:: pubs:187991
UUID:: uuid:0da6f1b9-1ea3-4362-b08d-cbd4cf6e0573
Local pid:: pubs:187991
Source identifiers:: 187991
Deposit date:: 2012-12-19

Terms of use

Copyright date:: 2008
Notes:: 12 pages

Licence:: Terms and Conditions of Use for Oxford University Research Archive

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