Mordell-Weil growth for GL2-type abelian varieties over Hilbert class fields of CM fields

2010/05/25 by David Hansen, David J. Hansen, Hansen, David
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Spectral Theory (math.SP) #math.NT #math.SP

paper · pdf · doi:10.48550/arxiv.1005.4700

13 pages; small changes and corrections made in v2; comments and corrections welcome

openalex publication_date 2010/05/25 · arxiv created 2010/06/10 · arxiv updated 2010/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a modular abelian variety of GL2-type over a totally real field F of class number one. Under some mild assumptions, we show that the Mordell-Weil rank of A grows polynomially over Hilbert class fields of CM extensions of F.

Citations

• Minoration du rang des courbes elliptiques sur les corps de classes de Hilbert

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