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Non-supersingular hyperelliptic jacobians

Yuri G. Zarhin (2004)

Bulletin de la Société Mathématique de France

Let K be a field of odd characteristic p , let f ( x ) be an irreducible separable polynomial of degree n 5 with big Galois group (the symmetric group or the alternating group). Let C be the hyperelliptic curve y 2 = f ( x ) and J ( C ) its jacobian. We prove that J ( C ) does not have nontrivial endomorphisms over an algebraic closure of K if either n 7 or p 3 .

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