Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Grossman-Naples, Doron
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223274616