Work

Polarized products of elliptic curves with complex multiplication and field of moduli Q

Year: 2024

Type: article

Abstract: Let 𝑅 be the maximal order in an imaginary quadratic field 𝐾.We give an equivalence of categories between the category of polarized abelian varieties isomorphic to a product of elliptic curves over C with complex multiplication (CM) by 𝑅 and the category of integral hermitian 𝑅-lattices.Then we apply this equivalence to enumerate all the genus 2 and 3 curves with field of moduli Q and with Jacobian isomorphic to a product of elliptic curves with CM by 𝑅.

Source: Polynesian Journal of Mathematics

DOI: 10.69763/polyjmath.1.5

Authors: Fabien Narbonne, Francesc Fité, Xavier Guitart

Institutions: Centre National de la Recherche Scientifique, Institut de recherche mathématique de Rennes, Université de Rennes, Universitat de Barcelona

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W4405634852

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Cites: 16

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Related to: 10