Non-supersingular hyperelliptic jacobians

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Abstract

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 y2 = 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.

Original languageEnglish (US)
Pages (from-to)617-634
Number of pages18
JournalBulletin de la Societe Mathematique de France
Volume132
Issue number4
DOIs
StatePublished - Jan 1 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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