Regular models of modular curves in prime level over ${\mathbb Z}_p^{\mathrm{ur}}$

Bas Edixhoven; Pierre Parent

Regular models of modular curves in prime level over ${\mathbb Z}_p^{\mathrm{ur}}$

Number Theory 2024-07-30 v2 Algebraic Geometry

Authors: Bas Edixhoven , Pierre Parent

Abstract

We give regular models for modular curves associated with (normalizer of) split and non-split Cartan subgroups of ${\mathrm{GL}}_2 ({\mathbb F}_p )$ (for $p$ any prime, $p\ge 5$ ). We then compute the group of connected components of the fiber at $p$ of the N\'eron model of their Jacobians.

Keywords

regular models modular curves Cartan subgroups Néron model Jacobians connected components

Cite

@article{arxiv.2211.01690,
  title  = {Regular models of modular curves in prime level over ${\mathbb Z}_p^{\mathrm{ur}}$},
  author = {Bas Edixhoven and Pierre Parent},
  journal= {arXiv preprint arXiv:2211.01690},
  year   = {2024}
}

Comments

While this work was in progress, B. E. passed away, on January 16, 2022. He is deeply missed. (P. P.) Version 2: minor corrections and improvements. To appear in Documenta Mathematica

Regular models of modular curves in prime level over ${\mathbb Z}_p^{\mathrm{ur}}$

Abstract

Keywords

Cite

Comments

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