23 citations · 108 across the 30 of their papers we have counts for
7 papers · 1 filter
Rank growth of elliptic curves over -th root extensions
Ari Shnidman, Ariel Weiss
Fix an elliptic curve over a number field and an integer which is a power of . We study the growth of the Mordell--Weil rank of after base change to the fields $…
Experiments with Ceresa classes of cyclic Fermat quotients
David T. -B. G. Lilienfeldt, Ari Shnidman
We give two new examples of non-hyperelliptic curves whose Ceresa cycles have torsion images in the intermediate Jacobian. For one of them, the central value of the -function of…
Sandpile groups of supersingular isogeny graphs
Nathanaël Munier, Ari Shnidman
Let and be distinct primes, and let be the -regular graph whose nodes are supersingular elliptic curves over and whose edges are…
A positive proportion of quartic fields are not monogenic yet have no local obstruction to being so
Levent Alpöge, Manjul Bhargava, Ari Shnidman
We show that a positive proportion of quartic fields are not monogenic, despite having no local obstruction to being monogenic. Our proof builds on the corresponding result for cub…
Ranks of abelian varieties in cyclotomic twist families
Ari Shnidman, Ariel Weiss
Let be an abelian variety over a number field , and suppose that embeds in , for some root of unity of order . Assum…
Elements of prime order in Tate-Shafarevich groups of abelian varieties over
Ari Shnidman, Ariel Weiss
For each prime , we show that there exist geometrically simple abelian varieties with non-trivial -torsion in their Tate-Shafarevich groups. Specifically, for a…
Genus two curves with full -level structure and Tate-Shafarevich groups
Nils Bruin, E. Victor Flynn, Ari Shnidman
We give an explicit rational parameterization of the surface over whose points parameterize genus 2 curves~ with full -level structure on…