Determination of all \(\mathbb{Q}\)-rational CM-points in the moduli space of principally polarized abelian surfaces

DOI10.1006/jabr.2000.8453zbMath0974.14015OpenAlexW2046106514MaRDI QIDQ1840617

Atsuki Umegaki, Naoki Murabayashi

Publication date: 12 June 2001

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

Full work available at URL: https://doi.org/10.1006/jabr.2000.8453

zbMATH Keywords

field of modulinumber of rational pointsprincipally polarized abelian surfaces\(\mathbb{Q}\)-rational CM-points

Mathematics Subject Classification ID

Rational points (14G05) Algebraic moduli of abelian varieties, classification (14K10) Class numbers, class groups, discriminants (11R29) Arithmetic ground fields for abelian varieties (14K15)

Related Items (6)

Icosahedral invariants and a construction of class fields via periods of \(K3\) surfaces ⋮ Computing the geometric endomorphism ring of a genus-2 Jacobian ⋮ Examples of CM curves of genus two defined over the reflex field ⋮ Principally polarized squares of elliptic curves with field of moduli equal to \(\mathbb{Q}\) ⋮ Endomorphism algebras of geometrically split abelian surfaces over \(\mathbb{Q} \) ⋮ Determination of simple CM abelian surfaces defined over \(\mathbb{Q}\)

Cites Work

• Unnamed Item
• CM-fields with cyclic ideal class groups of 2-power orders
• Examples of genus two CM curves defined over the rationals
• Determination of All Nonquadratic Imaginary Cyclic Number Fields of 2-Power Degrees with Ideal Class Groups of Exponents ≤2
• Determination of all non-quadratic imaginary cyclic number fields of 2-power degree with relative class number ≤ 20
• The field of moduli of abelian surfaces with complex multiplication.

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