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

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Keywords

Arithmetic of curves
Bad reduction
Probabilistic number theory
Rational points

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/s11139-025-01108-4

https://link.springer.com/content/pdf/10.1007/s11139-025-01108-4.pdfLicense: CC BY

Cite this

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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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AU - Lemke Oliver, Robert J.

AU - Loughran, Daniel

AU - Shnidman, Ari

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AB - 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.

KW - Arithmetic of curves

KW - Bad reduction

KW - Probabilistic number theory

KW - Rational points

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DO - 10.1007/s11139-025-01108-4

M3 - مقالة

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SN - 1382-4090

VL - 67

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 3

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Normal distribution of bad reduction

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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