A moduli interpretation for the non-split Cartan modular curve

Rebolledo, Marusia and Wuthrich, Christian (2018) A moduli interpretation for the non-split Cartan modular curve. Glasgow Mathematical Journal, 60 (2). pp. 411-434. ISSN 1469-509X

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Abstract

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].

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1017/S0017089517000180
Depositing User: Eprints, Support
Date Deposited: 20 Jun 2017 08:52
Last Modified: 02 Jul 2018 09:13
URI: http://eprints.nottingham.ac.uk/id/eprint/43660

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