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arXiv · 2108.07185

The Scheme of Monogenic Generators I: Representability

Sarah Arpin·Sebastian Bozlee·Leo Herr·Hanson Smith
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Abstract

This is the first in a series of two papers that study monogenicity of number rings from a moduli-theoretic perspective. Given an extension of algebras $B/A$, when is $B$ generated by a single element $\theta \in B$ over $A$? In this paper, we show there is a scheme $\mathcal{M}_{B/A}$ parameterizing the choice of a generator $\theta \in B$, a "moduli space" of generators. This scheme relates naturally to Hilbert schemes and configuration spaces. We give explicit equations and ample examples.

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Sarah Arpin, Sebastian Bozlee, Leo Herr, Hanson Smith. 2021-08-16. The Scheme of Monogenic Generators I: Representability. https://arxiv.org/abs/2108.07185

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