Hyperelliptic Jacobians with Real Multiplication

  title={Hyperelliptic Jacobians with Real Multiplication},
  author={Arsen Elkin},
Let K be a field of characteristic different from 2, and let f (x) be a sextic polynomial irreducible over K with no repeated roots, whose Galois group is A 5. If the Jacobian of the hyperelliptic curve y 2 = f (x) admits real multiplication over the ground field from an order of a real quadratic number field, then either its endomorphism algebra is this quadratic field or the Jacobian is supersingular. Let K be a field and K a an algebraic closure of K. Let f (x) ∈ K[x] be an irreducible… CONTINUE READING
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