Torsion points on hyperelliptic Jacobians via Anderson's $p$-adic soliton theory

Details Torsion points on hyperelliptic Jacobians via Anderson's $p$-adic soliton theory Torsion points on hyperelliptic Jacobians via Anderson's $p$-adic soliton theory

2011-11-12

arxiv.org/abs/1111.2973v1

Mathematics

Number Theory

16 pages

Scientific paper

We show that torsion points of certain orders are not on a theta divisor in
the Jacobian variety of a hyperelliptic curve given by the equation
$y^2=x^{2g+1}+x$ with $g \geq 2$. The proof employs a method of Anderson who
proved an analogous result for a cyclic quotient of a Fermat curve of prime
degree.

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