### Abstract

In a previous paper, the author proved that in characteristic zero the jacobian J(C) of a hyperelliptic curve C : y^{2} = f(x) has only trivial endomorphisms over an algebraic closure K_{a} of the ground field K if the Galois group Gal(f) of the irreducible polynomial f(x) ∈ K[x] is either the symmetric group S_{n} or the alternating group A_{n}. Here n > 4 is the degree of f. In another paper by the author this result was extended to the case of certain "smaller" Galois groups. In particular, the infinite series n = 2^{r} + 1, Gal(f) = L_{2}(2_{r}) := PSL_{2}(F_{2r}) and n = 2^{4r+2} + 1, Gal(f) = Sz(2^{2r+1}) were treated. In this paper the case of Gal(f) = U_{3}(2^{m}) := PSU_{3}(F_{2m}) and n = 2^{3m} + 1 is treated.

Original language | English (US) |
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Pages (from-to) | 95-102 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 131 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2003 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics