Genus $0$ Modular curves of prime power level with a point defined over number fields other than $\Q$

Rakvi

Genus $0$ Modular curves of prime power level with a point defined over number fields other than $\Q$

Number Theory 2022-08-05 v1

Authors: Rakvi

Abstract

Associated to an open subgroup $G$ of $\GL_2(\Zhat)$ satisfying conditions $-I \in G$ and $\det(G) \subsetneq (\Zhat)^{\times}$ there is a modular curve $X_G$ which is a smooth compact curve defined over an extension of $\Q.$ In this article, we give a complete list of all such prime power level genus $0$ modular curves with a point.

Keywords

modular curves genus 0 prime power level open subgroup of gl2 number fields smooth compact curve

Cite

@article{arxiv.2208.02452,
  title  = {Genus $0$ Modular curves of prime power level with a point defined over number fields other than $\Q$},
  author = {Rakvi},
  journal= {arXiv preprint arXiv:2208.02452},
  year   = {2022}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2105.14623

Genus $0$ Modular curves of prime power level with a point defined over number fields other than $\Q$

Abstract

Keywords

Cite

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