Let be a non-constant morphism from a curve to an abelian variety , all defined over a number field . Suppose that is a counterexample to the Hasse principle. We give sufficient conditions for the failure of the Hasse principle on to be accounted for by the Brauer–Manin obstruction. These sufficiency conditions are slightly stronger than assuming that and are finite.
Soit un morphisme (qui n’est pas constant) d’une courbe vers une variété abélienne , tous définis sur un corps de nombres . Supposons que ne satisfait pas le principe de Hasse. Nous donnons des conditions suffisantes pour que l’obstruction de Brauer-Manin soit la seule obstruction au principe de Hasse. Ces conditions suffisantes sont légèrement plus fortes que de supposer que et sont finis.
@article{JTNB_2004__16_3_773_0, author = {Siksek, Samir}, title = {The {Brauer{\textendash}Manin} obstruction for curves having split {Jacobians}}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {773--777}, publisher = {Universit\'e Bordeaux 1}, volume = {16}, number = {3}, year = {2004}, doi = {10.5802/jtnb.469}, zbl = {1076.14033}, mrnumber = {2144966}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.469/} }
TY - JOUR AU - Siksek, Samir TI - The Brauer–Manin obstruction for curves having split Jacobians JO - Journal de théorie des nombres de Bordeaux PY - 2004 SP - 773 EP - 777 VL - 16 IS - 3 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.469/ DO - 10.5802/jtnb.469 LA - en ID - JTNB_2004__16_3_773_0 ER -
%0 Journal Article %A Siksek, Samir %T The Brauer–Manin obstruction for curves having split Jacobians %J Journal de théorie des nombres de Bordeaux %D 2004 %P 773-777 %V 16 %N 3 %I Université Bordeaux 1 %U http://archive.numdam.org/articles/10.5802/jtnb.469/ %R 10.5802/jtnb.469 %G en %F JTNB_2004__16_3_773_0
Siksek, Samir. The Brauer–Manin obstruction for curves having split Jacobians. Journal de théorie des nombres de Bordeaux, Volume 16 (2004) no. 3, pp. 773-777. doi : 10.5802/jtnb.469. http://archive.numdam.org/articles/10.5802/jtnb.469/
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