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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 


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).


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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