On the variation of the rank of Jacobian varieties on unramified abelian towers over number fields

2003/10/08 by Amílcar Pacheco, Amilcar Pacheco, Pacheco, Amilcar
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.math/0310123

11 pages, revised version

openalex publication_date 2003/10/08 · arxiv created 2003/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C be a smooth projective curve defined over a number field k, X/k(C) a smooth projective curve of positive genus, J_X the Jacobian variety of X and (τ,B) the k(C)/k-trace of J_X. We estimate how the rank of J_X(k(C))/τB(k) varies when we take an unramified abelian cover π:C'→ C defined over k.

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