Normal distribution of bad reduction
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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>100</mml:mn> <mml:mo>%</mml:mo></mml:mrow> </mml:math> of curves in these families have, in a precise sense, many such primes.
Authors
- Daniel Loughran (ORCID: https://orcid.org/0000-0001-5892-1564)
- Robert J. Lemke Oliver (ORCID: https://orcid.org/0000-0002-7170-051X)
- Ari Shnidman
Institutions
- Tufts University (US)
- Hebrew University of Jerusalem (IL)
- University of Bath (GB)
Publication Details
- Journal
- The Ramanujan Journal
- Published
- 2025-05-22
- DOI
- https://doi.org/10.1007/s11139-025-01108-4
- Primary Topic
- Analytic Number Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- UK Research and Innovation
- European Commission
- Israel Science Foundation
- European Research Council