Endomorphism algebras of hyperelliptic jacobians and finite projective lines

2005/08/06 by Arsen Elkin, Elkin, Arsen, Yuri G. Zarhin +1
Computer Science · Mathematics · #11G10 #11G30 #14H40 #14K05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.AG #math.NT #msc:11G10 #msc:11G30 #msc:14H40 #msc:14K05

paper · pdf · doi:10.48550/arxiv.math/0508120

LaTeX, 16 pages

openalex publication_date 2005/08/06 · arxiv created 2008/06/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the jacobian of a hyperelliptic curve y²=f(x) is absolutely simple if deg(f)=q+1 where q is a power prime congruent to 5 modulo 8, the polynomial f(x) is irreducible over the ground field of characteristic zero and its Galois group is L₂(q).

Citations

• Homomorphisms of abelian varieties
• Hyperelliptic jacobians with real multiplication

Related

• Hyperelliptic jacobians and projective linear Galois groups
• Hyperelliptic jacobians without complex multiplication, doubly transitive permutation groups and projective representations
• Non-supersingular Hyperelliptic jacobians
• Superelliptic jacobians
• Hyperelliptic jacobians without complex multiplication