For a curve of genus defined over a finite field, we present a sufficient criterion for the non-existence of automorphisms of order a power of a rational prime. We show how this criterion can be used to determine the automorphism group of some modular curves of high genus.
Pour une courbe de genre définie sur un corps fini, nous présentons un critère suffisant pour la non-existence d’automorphismes de l’ordre une puissance d’un nombre premier. Nous montrons comment ce critère peut être utilisé pour déterminer le groupe d’automorphismes de certaines courbes modulaires de genres supérieurs.
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Mots-clés : Automorphisms of curves, non-split Cartan modular curves
Josep González 1

@article{JTNB_2017__29_2_535_0, author = {Josep Gonz\'alez}, title = {Constraints on the automorphism group of a curve}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {535--548}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {29}, number = {2}, year = {2017}, doi = {10.5802/jtnb.990}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.990/} }
TY - JOUR AU - Josep González TI - Constraints on the automorphism group of a curve JO - Journal de théorie des nombres de Bordeaux PY - 2017 SP - 535 EP - 548 VL - 29 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.990/ DO - 10.5802/jtnb.990 LA - en ID - JTNB_2017__29_2_535_0 ER -
%0 Journal Article %A Josep González %T Constraints on the automorphism group of a curve %J Journal de théorie des nombres de Bordeaux %D 2017 %P 535-548 %V 29 %N 2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.990/ %R 10.5802/jtnb.990 %G en %F JTNB_2017__29_2_535_0
Josep González. Constraints on the automorphism group of a curve. Journal de théorie des nombres de Bordeaux, Volume 29 (2017) no. 2, pp. 535-548. doi : 10.5802/jtnb.990. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.990/
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