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arXiv · 2610.30376

Isogenies of Oriented Elliptic Curves

Doron Grossman-Naples
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Abstract

We construct and describe the moduli stack $\mathrm{Isog}$ of isogenies between oriented elliptic curves. We show that $\mathrm{Isog}$ is a spectral Deligne-Mumford stack and a relative spectral algebraic space over $\mathcal{M}_{\mathrm{ell}}^{\mathrm{or}}$, and give a fiber product decomposition of $\mathrm{Isog}$ 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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BibTeXRIS

Doron Grossman-Naples. 2026-10-21. Isogenies of Oriented Elliptic Curves. https://arxiv.org/abs/2610.30376

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