3 papers
math.NT2022
Powers of the Cartier operator on Artin-Schreier covers
Steven R. Groen
Curves in positive characteristic have a Cartier operator acting on their space of regular differentials. The -number of a curve is defined to be the dimension of the kernel of…
math.NT2021
A parametrized set of explicit elements of $\Sha(E/\Q)[3]$
Steven R. Groen, Jaap Top
In this paper, we give explicit equations for homogeneous spaces corresponding to a rational isogeny of degree . An explicit set of elliptic curves with elements of order in…
math.NT2021
Doubly isogenous genus-2 curves with -action
Vishal Arul, Jeremy Booher, Steven R. Groen +5
We study the extent to which curves over finite fields are characterized by their zeta functions and the zeta functions of certain of their covers. Suppose C and C' are curves over…