Normal distribution of bad reduction

Robert J. Lemke Oliver; Daniel Loughran; Ari Shnidman

doi:10.1007/s11139-025-01108-4

Normal distribution of bad reduction

Robert J. Lemke Oliver, Daniel Loughran, Ari Shnidman

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We prove normal distribution laws for primes of bad semistable reduction in families of curves. As a consequence, we deduce that when ordered by height, 100% of curves in these families have, in a precise sense, many such primes.

Original language	English
Article number	52
Journal	The Ramanujan Journal
Volume	67
Early online date	22 May 2025
DOIs	https://doi.org/10.1007/s11139-025-01108-4
Publication status	Published - 22 May 2025

Data Availability Statement

Not applicable.

Funding

Robert Lemke Oliver is supported by the National Science Foundation grant DMS-2200760 and by a Simons Fellowship in Mathematics. Daniel Loughran is supported by UKRI Future Leaders Fellowship MR/V021362/1. Ari Shnidman was funded by the European Union (ERC, CurveArithmetic, 101078157) and the Israel Science Foundation (grant No. 2301/20).

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10.1007/s11139-025-01108-4Licence: CC BY

https://arxiv.org/abs/2305.15874Licence: CC BY

Fellowship FLF Geometric Analytic Number Theory
Loughran, D. (PI)
UK Research & Innovation
1/10/21 → 30/09/25
Project: Research council

Cite this

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Normal distribution of bad reduction

Abstract

Data Availability Statement

Funding

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Projects

Fellowship FLF Geometric Analytic Number Theory

Cite this