The cuspidal torsion packet on hyperelliptic Fermat quotients | CU Experts

; Let; ; ; ℓ; ≥; 7; ; ; be a prime,; ; C; ; be the non-singular projective curve defined over; ; ℚ; ; by the affine model; ; ; y; ; (; 1; -; y; ); ; =; ; x; ℓ; ; ; ; ,; ; ∞; ; the point of; ; C; ; at infinity on this model,; ; J; ; the Jacobian of; ; C; ; , and; ; ; φ; :; C; →; J; ; ; the albanese embedding with; ; ∞; ; as base point. Let; ; ; ℚ; ¯; ; ; be an algebraic closure of; ; ℚ; ; . Taking care of a case not covered in [12], we show that; ; ; φ; ; (; C; ); ; ∩; ; J; tors; ; ; (; ; ℚ; ¯; ; ); ; ; ; consists only of the image under; ; φ; ; of the Weierstrass points of; ; C; ; and the points; ; ; (; x; ,; y; ); =; (; 0; ,; 0; ); ; ; and; ; ; (; 0; ,; 1; ); ; ; , where; ; ; J; tors; ; ; denotes the torsion points of; ; J; ; .;

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