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A moduli interpretation for the non-split Cartan modular curve

Rebolledo, Marusia; Wuthrich, Christian

A moduli interpretation for the non-split Cartan modular curve Thumbnail


Marusia Rebolledo


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 X+ nsp(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 [Che98, Che00].

Journal Article Type Article
Acceptance Date Jun 16, 2017
Online Publication Date Oct 30, 2017
Publication Date May 1, 2018
Deposit Date Jun 20, 2017
Publicly Available Date Oct 30, 2017
Journal Glasgow Mathematical Journal
Print ISSN 0017-0895
Electronic ISSN 1469-509X
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 60
Issue 2
Public URL
Publisher URL


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