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Isogenies of Oriented Elliptic Curves

  • Doron Grossman-Naples
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Abstract

We construct and describe the moduli stack Isog of isogenies between oriented elliptic curves. We show that Isog is a spectral Deligne-Mumford stack and a relative spectral algebraic space over ℳellor, and give a fiber product decomposition of Isog corresponding to a connected-étale factorization on oriented elliptic curves. In the process of proving these results, we construct a theory of duality and quotients for spectral abelian varieties, prove a higher-algebraic version of Nakayama's lemma, and lift the rigidity theorem for morphisms of elliptic curves to the setting of spectral algebraic geometry.

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Cite

BibTeXRIS
BibTeX
@misc{grossmannaples2026isogenies,
  title = {{Isogenies of Oriented Elliptic Curves}},
  author = {Doron Grossman-Naples},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30376},
  eprint = {2610.30376},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30376},
}
RIS
TY  - UNPB
TI  - Isogenies of Oriented Elliptic Curves
AU  - Doron Grossman-Naples
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.30376
UR  - https://arxiv.org/abs/2610.30376
AB  - We construct and describe the moduli stack Isog of isogenies between oriented elliptic curves. We show that Isog is a spectral Deligne-Mumford stack and a relative spectral algebraic space over ℳ_ell^or, and give a fiber product decomposition of Isog corresponding to a connected-étale factorization on oriented elliptic curves. In the process of proving these results, we construct a theory of duality and quotients for spectral abelian varieties, prove a higher-algebraic version of Nakayama's lemma, and lift the rigidity theorem for morphisms of elliptic curves to the setting of spectral algebraic geometry.
ER  -