Fields of definition of elliptic $k$-curves and the realizability of all genus 2 Sato–Tate groups over a number field

DOI10.1090/tran/7074zbMath1432.11059arXiv1511.02322OpenAlexW2281004135MaRDI QIDQ4635473

Xavier Guitart, Francesc Fité

Publication date: 23 April 2018

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.02322

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Complex multiplication and moduli of abelian varieties (11G15) Complex multiplication and abelian varieties (14K22)

Related Items (5)

Sato–Tate groups of abelian threefolds: a preview of the classification ⋮ On a local-global principle for quadratic twists of abelian varieties ⋮ Principally polarized squares of elliptic curves with field of moduli equal to \(\mathbb{Q}\) ⋮ Endomorphism algebras of geometrically split abelian surfaces over \(\mathbb{Q} \) ⋮ Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of \(\mathrm{GL}_2\)-type

Uses Software

• Magma
• PARI/GP
• SageMath
• LMFDB

Cites Work

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• On the arithmetic of abelian varieties

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