科研之友
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摘要
Modular curves like X-0(N) and X-1(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 allowfor 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 X-nsp(p) and X-nsp(+)(p) associated to non-split Cartan subgroups and their normaliser in GL(2)(F-p). 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).
- 出版日期2018-5
