Semistable abelian varieties over Z[1/6] and Z[1/10]

2001/03/03 by Frank Calegari, Calegari, Frank
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT

paper · pdf · doi:10.48550/arxiv.math/0103240

arxiv created 2001/03/03 · openalex publication_date 2001/03/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Continuing on from recent results of Brumer-Kramer and of Schoof, we show that there exist non-zero semistable Abelian varieties over Z[1/N], with N squarefree, if and only if N is not in the set 1,2,3,5,6,7,10,13. Our results are contingent on the GRH discriminant bounds of Odlyzko.

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