Geodesic
A MODULI INTERPRETATION FOR THE NON-SPLIT CARTAN MODULAR CURVE
Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 411-434

Voir la notice de l'article provenant de la source Cambridge University Press

Modular curves like X0(N) and X1(N) appear very frequently in arithmetic geometry. While their complex points are obtained as a quotient of the upper half plane by some subgroups of SL2(Z), they allow for a more arithmetic description as a solution to a moduli problem. We wish to give such a moduli description for two other modular curves, denoted here by Xnsp(p) and Xnsp+(p) associated to non-split Cartan subgroups and their normaliser in GL2(Fp). These modular curves appear for instance in Serre's problem of classifying all possible Galois structures of p-torsion points on elliptic curves over number fields. We give then a moduli-theoretic interpretation and a new proof of a result of Chen (Proc. London Math. Soc. (3) 77(1) (1998), 1–38; J. Algebra 231(1) (2000), 414–448). 
REBOLLEDO, MARUSIA; WUTHRICH, CHRISTIAN. A MODULI INTERPRETATION FOR THE NON-SPLIT CARTAN MODULAR CURVE. Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 411-434. doi: 10.1017/S0017089517000180
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