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Endomorphism algebras of hyperelliptic jacobians and finite projective lines

Arsen Elkin·Yuri G. Zarhin
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Abstract

We prove that the jacobian of a hyperelliptic curve y^2=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 L_2(q).

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Arsen Elkin, Yuri G. Zarhin. 2008-06-20. Endomorphism algebras of hyperelliptic jacobians and finite projective lines. https://arxiv.org/abs/math/0508120

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