A finiteness theorem for abelian varieties with totally bad reduction

2021/10/02 by Plawan Das, Das, Plawan, C. S. Rajan +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2110.00870

openalex publication_date 2021/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that up to potential isogeny, there are only finitely many abelian varieties of dimension d defined over a number field K, such that for any finite place v outside a fixed finite set S of places of K containing the archimedean places, it has either good reduction at v, or totally bad reduction at v and good reduction over a quadratic extension of the completion of K at v.

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