The arithmetic of QM-abelian surfaces through their Galois representations

DOI10.1016/J.JALGEBRA.2004.07.019zbMath1064.11043arXivmath/0303162OpenAlexW2055805885MaRDI QIDQ706001

Luis V. Dieulefait, Victor Rotger

Publication date: 16 February 2005

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0303162

zbMATH Keywords

abelian varietiesGalois representationsTate modulesquaternionic multiplicationarithmetic algebraic geometryarithmetic abelian surfacesquaternionic algebras

Mathematics Subject Classification ID

Galois theory (11R32) Abelian varieties of dimension (> 1) (11G10) Varieties over global fields (11G35) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Global ground fields in algebraic geometry (14G25) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (4)

Explicit surjectivity of Galois representations for abelian surfaces and \(\operatorname{GL}_{2}\)-varieties ⋮ Endomorphism algebras of QM abelian surfaces ⋮ Simplicity of twists of abelian varieties ⋮ Surface abéliennes à multiplication quaternionique munie d'une structure de niveau Γ₀(N)

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