Finite flat group schemes over Z killed by 19

Lassina Dembélé; René Schoof

doi:10.1016/j.jnt.2024.02.008

Finite flat group schemes over Z killed by 19

Lassina Dembélé^*, René Schoof

^*Corresponding author for this work

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

Abstract

Since simple commutative finite flat group schemes over Z are killed by a prime number p, their order is a power of p. Abraškin and Fontaine have both shown that for primes p⩽17 the only simple p-power order group schemes are μ_p and Z/pZ. We extend their result to p=19.

Original language	English
Pages (from-to)	191-195
Number of pages	5
Journal	Journal of Number Theory
Volume	260
DOIs	https://doi.org/10.1016/j.jnt.2024.02.008
Publication status	Published - Jul 2024

Keywords

Finite group schemes
Number fields

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10.1016/j.jnt.2024.02.008

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title = "Finite flat group schemes over Z killed by 19",

abstract = "Since simple commutative finite flat group schemes over Z are killed by a prime number p, their order is a power of p. Abra{\v s}kin and Fontaine have both shown that for primes p⩽17 the only simple p-power order group schemes are μp and Z/pZ. We extend their result to p=19.",

keywords = "Finite group schemes, Number fields",

author = "Lassina Demb{\'e}l{\'e} and Ren{\'e} Schoof",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier Inc.",

year = "2024",

month = jul,

doi = "10.1016/j.jnt.2024.02.008",

language = "English",

volume = "260",

pages = "191--195",

journal = "Journal of Number Theory",

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T1 - Finite flat group schemes over Z killed by 19

AU - Dembélé, Lassina

AU - Schoof, René

PY - 2024/7

Y1 - 2024/7

N2 - Since simple commutative finite flat group schemes over Z are killed by a prime number p, their order is a power of p. Abraškin and Fontaine have both shown that for primes p⩽17 the only simple p-power order group schemes are μp and Z/pZ. We extend their result to p=19.

AB - Since simple commutative finite flat group schemes over Z are killed by a prime number p, their order is a power of p. Abraškin and Fontaine have both shown that for primes p⩽17 the only simple p-power order group schemes are μp and Z/pZ. We extend their result to p=19.

KW - Finite group schemes

KW - Number fields

UR - http://www.scopus.com/inward/record.url?scp=85188458492&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2024.02.008

DO - 10.1016/j.jnt.2024.02.008

M3 - Article

AN - SCOPUS:85188458492

SN - 0022-314X

VL - 260

SP - 191

EP - 195

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Finite flat group schemes over Z killed by 19

Abstract

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