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Comptes Rendus Mathématique
Volume 338, n° 1
pages 47-50 (janvier 2004)
Doi : 10.1016/j.crma.2003.10.034
Received : 30 April 2003 ;  accepted : 21 October 2003
An analogue for elliptic curves of the Grunwald-Wang example

Roberto  Dvornicich a ,  Umberto  Zannier b
aDipartimento di Matematica, Università di Pisa, via Buonarroti, 2, 56127 Pisa, Italy 
bIstituto Universitario di Architettura D.C.A. S.Croce, 191 (Tolentini), 30135 Venezia, Italy 

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We give examples of elliptic curves   and rational points   such that   is divisible by   in   for each rational place   but   is not divisible by   in  . This is an analogue of a well-known example, with   in place of  : namely,   is a rational  -th power locally almost everywhere, but not globally in  . To cite this article: R. Dvornicich, U. Zannier, C. R. Acad. Sci. Paris, Ser. I 338 (2004).

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Nous donnons des exemples de courbes elliptiques   et de points rationnels   tels que   soit divisible par   dans   pour tout place rationnelle  , sans que   soit divisible par   dans  . Il s'agit d'un analogue d'un exemple bien connu, avec   à la place de   : on sait que, dans  ,   est localement une puissance  -ième presque partout, mais   n'est pas une puissance  -ième globalement. Pour citer cet article : R. Dvornicich, U. Zannier, C. R. Acad. Sci. Paris, Ser. I 338 (2004).




© 2003  Académie des sciences@@#104156@@

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