3 papers
math.NT2021
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…
math.NT2020
A positive proportion of cubic 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 cubic fields are not monogenic, despite having no local obstruction to being monogenic. Our proof involves the comparison of -descent and $…
math.NT2017
Quadratic twists of abelian varieties with real multiplication
Ari Shnidman
Let be a totally real number field and a principally polarized abelian variety with real multiplication by the ring of integers of a totally real field. Ass…