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

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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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     title = {A {MODULI} {INTERPRETATION} {FOR} {THE} {NON-SPLIT} {CARTAN} {MODULAR} {CURVE}},
     journal = {Glasgow mathematical journal},
     pages = {411--434},
     year = {2018},
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     doi = {10.1017/S0017089517000180},
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