We give a criterion, based on the automorphism group, for certain cyclic covers of the projective line to be defined over their field of moduli. An example of a cyclic cover of the complex projective line with field of moduli that can not be defined over is also given.
Nous donnons un critère, dépendant du groupe des automorphismes, pour que certains revêtements cycliques de la droite projective soient définis sur leur corps de modules. Nous donnons aussi un exemple de revêtement cyclique de la droite projective complexe de corps de module qui ne peut pas être défini sur .
@article{JTNB_2009__21_3_679_0, author = {Kontogeorgis, Aristides}, title = {Field of moduli versus field of definition for cyclic covers of the projective line}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {679--693}, publisher = {Universit\'e Bordeaux 1}, volume = {21}, number = {3}, year = {2009}, doi = {10.5802/jtnb.694}, zbl = {1201.14020}, mrnumber = {2605539}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.694/} }
TY - JOUR AU - Kontogeorgis, Aristides TI - Field of moduli versus field of definition for cyclic covers of the projective line JO - Journal de théorie des nombres de Bordeaux PY - 2009 SP - 679 EP - 693 VL - 21 IS - 3 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.694/ DO - 10.5802/jtnb.694 LA - en ID - JTNB_2009__21_3_679_0 ER -
%0 Journal Article %A Kontogeorgis, Aristides %T Field of moduli versus field of definition for cyclic covers of the projective line %J Journal de théorie des nombres de Bordeaux %D 2009 %P 679-693 %V 21 %N 3 %I Université Bordeaux 1 %U http://archive.numdam.org/articles/10.5802/jtnb.694/ %R 10.5802/jtnb.694 %G en %F JTNB_2009__21_3_679_0
Kontogeorgis, Aristides. Field of moduli versus field of definition for cyclic covers of the projective line. Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 3, pp. 679-693. doi : 10.5802/jtnb.694. http://archive.numdam.org/articles/10.5802/jtnb.694/
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