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PreprintarXiv licencearXiv

Atkin--Lehner Quotients of Modular Curves at Primes of Bad Reduction

  • Lea Beneish
  • Boya Wen
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Abstract

Let N be a square-free, positive integer and let p≥ 5 be a prime dividing N. In this work, we construct semistable models of Atkin--Lehner quotients of X0(N) over the Witt ring W(𝔽̅p) by taking the corresponding quotients of the Deligne--Rapoport model of X0(N). We give an explicit description of the special fiber of the models and obtain genus formulae for the Atkin--Lehner quotients of X0(N).

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Cite

BibTeXRIS
BibTeX
@misc{beneish2026atkinlehner,
  title = {{Atkin--Lehner Quotients of Modular Curves at Primes of Bad Reduction}},
  author = {Lea Beneish and Boya Wen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39725},
  eprint = {2609.39725},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39725},
}
RIS
TY  - UNPB
TI  - Atkin--Lehner Quotients of Modular Curves at Primes of Bad Reduction
AU  - Lea Beneish
AU  - Boya Wen
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39725
UR  - https://arxiv.org/abs/2609.39725
AB  - Let N be a square-free, positive integer and let p≥ 5 be a prime dividing N. In this work, we construct semistable models of Atkin--Lehner quotients of X_0(N) over the Witt ring W(𝔽̅_p) by taking the corresponding quotients of the Deligne--Rapoport model of X_0(N). We give an explicit description of the special fiber of the models and obtain genus formulae for the Atkin--Lehner quotients of X_0(N).
ER  -