November 8, 2025Open Access

Abelian threefolds with imaginary multiplication

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Analysis shows class number constraints in abelian threefolds, indicating connections to elliptic curves and complex multiplication in number fields.

Class number bounds in abelian threefolds relate to their Galois representations and elliptic curves.
Key relationship is derived by connecting Galois representations to Hecke characters of elliptic curves.
Geometric endomorphism algebra shows significant implications for abelian threefolds over number fields.
Indicates how the class number is affected by parameters related to complex multiplication.

Fité et al. (2025) studied this question.

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Analysis shows class number constraints in abelian threefolds, indicating connections to elliptic curves and complex multiplication in number fields.