Journal of the Ramanujan Mathematical Society

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Endomorphism Algebras of Hyperelliptic Jacobians and Finite Projective Lines II


Affiliations
1 Department of Mathematics, Colorado State University, Fort Collins, CO 80523, United States
2 Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States
     

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We prove that the jacobian of a hyperelliptic curve y2=f(x) is either absolutely simple or isogenous to a self-product of a CM elliptic curve if deg (f)=q+1 where q is a power prime congruent to 7 modulo 8, the polynomial f(x) is irreducible over the ground field of characteristic zero and its Galois group is L2(q).
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  • Endomorphism Algebras of Hyperelliptic Jacobians and Finite Projective Lines II

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Authors

Arsen Elkin
Department of Mathematics, Colorado State University, Fort Collins, CO 80523, United States
Yuri G. Zarhin
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States

Abstract


We prove that the jacobian of a hyperelliptic curve y2=f(x) is either absolutely simple or isogenous to a self-product of a CM elliptic curve if deg (f)=q+1 where q is a power prime congruent to 7 modulo 8, the polynomial f(x) is irreducible over the ground field of characteristic zero and its Galois group is L2(q).