We prove that the Abelian K-surfaces whose endomorphism algebra is a rational quaternion algebra are parametrized, up to isogeny, by the K-rational points of the quotient of certain Shimura curves by the group of their Atkin–Lehner involutions.
Nous démontrons que les K-surfaces abéliennes dont l'algèbre d'endomorphismes est une algèbre de quaternions sont paramétrisées, à isogénie près, par les points K-rationnels du quotient de certaines courbes de Shimura par le groupe de leurs involutions d'Atkin–Lehner.
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@article{CRMATH_2009__347_23-24_1325_0, author = {Guitart, Xavier and Molina, Santiago}, title = {Parametrization of {Abelian} {\protect\emph{K}-surfaces} with quaternionic multiplication}, journal = {Comptes Rendus. Math\'ematique}, pages = {1325--1330}, publisher = {Elsevier}, volume = {347}, number = {23-24}, year = {2009}, doi = {10.1016/j.crma.2009.09.025}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.09.025/} }
TY - JOUR AU - Guitart, Xavier AU - Molina, Santiago TI - Parametrization of Abelian K-surfaces with quaternionic multiplication JO - Comptes Rendus. Mathématique PY - 2009 SP - 1325 EP - 1330 VL - 347 IS - 23-24 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.09.025/ DO - 10.1016/j.crma.2009.09.025 LA - en ID - CRMATH_2009__347_23-24_1325_0 ER -
%0 Journal Article %A Guitart, Xavier %A Molina, Santiago %T Parametrization of Abelian K-surfaces with quaternionic multiplication %J Comptes Rendus. Mathématique %D 2009 %P 1325-1330 %V 347 %N 23-24 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.09.025/ %R 10.1016/j.crma.2009.09.025 %G en %F CRMATH_2009__347_23-24_1325_0
Guitart, Xavier; Molina, Santiago. Parametrization of Abelian K-surfaces with quaternionic multiplication. Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1325-1330. doi : 10.1016/j.crma.2009.09.025. http://www.numdam.org/articles/10.1016/j.crma.2009.09.025/
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