V. Arul

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20182021

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math.AG2019

Torsion points on Fermat quotients of the form $y^{n} = x^{d} + 1$

Vishal Arul

We classify all geometric torsion points on the Fermat quotients $y^{n} = x^{d} + 1$ where $n, d \geq 2$ are coprime. In addition, we classify all geometric torsion points on the generi…

math.AG2018

Division by $1 - ζ$ on superelliptic curves and jacobians

Vishal Arul

In 2016, Yuri Zarhin gave formulas for "dividing a point on a hyperelliptic curve by 2." Given a point $P$ on a hyperelliptic curve $C$ , Zarhin gives the Mumford's repres…

Torsion points on Fermat quotients of the form yn=xd+1

Division by 1−ζ on superelliptic curves and jacobians

Torsion points on Fermat quotients of the form $y^{n} = x^{d} + 1$

Division by $1 - ζ$ on superelliptic curves and jacobians