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- Title
On the simplicity of Jacobians for hyperelliptic curves of genus 2 over the field of rational numbers with torsion points of high order.
- Authors
Platonov, V.; Zhgun, V.; Petrunin, M.
- Abstract
The article focuses on simple Jacobians for Genus 2 hyperelliptic curves over the rational number field with high order torsion points. It proves the simplicity of Jacobian through a method based on Frobenius endomorphism characteristic polynomial properties and another method based on simple Abelian variety characterization. It points out that the second method is more effective than the first one due to the involvement of the analytic Abelian variety representation and the complex number field.
- Subjects
JACOBIAN matrices; ALGEBRAIC curves; ALGEBRAIC geometry; FUNCTIONS of several complex variables; JACOBIAN determinants; RATIONAL numbers; ABELIAN varieties; FROBENIUS manifolds; ENDOMORPHISMS
- Publication
Doklady Mathematics, 2013, Vol 87, Issue 3, p318
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562413030216