In a previous paper, the author proved that in characteristic zero the jacobian J(C) of a hyperelliptic curve C : y2 = f(x) has only trivial endomorphisms over an algebraic closure Ka of the ground field K if the Galois group Gal(f) of the irreducible polynomial f(x) ∈ K[x] is either the symmetric group Sn or the alternating group An. 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 = 2r + 1, Gal(f) = L2(2r) := PSL2(F2r) and n = 24r+2 + 1, Gal(f) = Sz(22r+1) were treated. In this paper the case of Gal(f) = U3(2m) := PSU3(F2m) and n = 23m + 1 is treated.
All Science Journal Classification (ASJC) codes
- Applied Mathematics