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Number theory - 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 d...

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Authors


Zannier, U More by this author
Journal:
Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Volume:
19
Issue:
2
Pages:
149-162
Publication date:
2008
EISSN:
1720-0768
ISSN:
1120-6330
URN:
uuid:682a7a47-0781-41f7-a554-67908a68529a
Source identifiers:
189846
Local pid:
pubs:189846

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