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September 10, 2025Transactions of the London Mathematical SocietyOpen Access

Explicit height estimates for CM curves of genus 2

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Explicit constants were derived for bounding the discriminant of cyclic Galois CM fields.
The study simplifies existing arguments related to the bounds of genus 2 curves.
Focusing on potentially good reduction, the research considers specific predefined sets of primes.
The findings help clarify the relationship between height estimates and CM curves.

Implication

The paper reveals explicit estimates for height in genus 2 CM curves, suggesting refined bounds on discriminants in Galois fields.

Abstract

In this paper, we make explicit the constants of Habegger and Pazuki's work from 2017 on bounding the discriminant of cyclic Galois CM fields corresponding to genus 2 curves with CM and potentially good reduction outside a predefined set of primes. We also simplify some of the arguments.

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Cite This Study

Frey et al. (2025) studied this question.

synapsesocial.com/papers/68c1d7fe54b1d3bfb60fa642 https://doi.org/10.1112/tlm3.70013

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Implication

The paper reveals explicit estimates for height in genus 2 CM curves, suggesting refined bounds on discriminants in Galois fields.

Explicit height estimates for CM curves of genus 2

Key Points

Implication

Abstract

Discussion

Cite This Study

Explicit height estimates for CM curves of genus 2

Key Points

Implication

Abstract

Discussion

Cite This Study

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