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

^*Corresponding author for this work

Einstein Institute of Mathematics

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	Ramanujan Journal
Volume	67
Issue number	3
DOIs	https://doi.org/10.1007/s11139-025-01108-4
State	Published - Jul 2025

Bibliographical note

Publisher Copyright:
© The Author(s) 2025.

Keywords

Arithmetic of curves
Bad reduction
Probabilistic number theory
Rational points

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10.1007/s11139-025-01108-4

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title = "Normal distribution of bad reduction",

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.",

keywords = "Arithmetic of curves, Bad reduction, Probabilistic number theory, Rational points",

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doi = "10.1007/s11139-025-01108-4",

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KW - Arithmetic of curves

KW - Bad reduction

KW - Probabilistic number theory

KW - Rational points

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Normal distribution of bad reduction

Abstract

Bibliographical note

Keywords

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