TY - UNPB

T1 - Cubic and quartic points on modular curves using generalised symmetric Chabauty

AU - Box, Josha

AU - Gajovic, Stevan

AU - Goodman, Pip

PY - 2021/2/16

Y1 - 2021/2/16

N2 - Answering a question of Zureick-Brown, we determine the cubic points on the modular curves X0(N) for N∈{53,57,61,65,67,73} as well as the quartic points on X0(65). To do so, we develop a "partially relative" symmetric Chabauty method. Our results generalise current symmetric Chabauty theorems, and improve upon them by lowering the involved prime bound. For our curves a number of novelties occur. We prove a "higher order" Chabauty theorem to deal with these cases. Finally, to study the isolated quartic points on X0(65), we rigorously compute the full rational Mordell--Weil group of its Jacobian.

AB - Answering a question of Zureick-Brown, we determine the cubic points on the modular curves X0(N) for N∈{53,57,61,65,67,73} as well as the quartic points on X0(65). To do so, we develop a "partially relative" symmetric Chabauty method. Our results generalise current symmetric Chabauty theorems, and improve upon them by lowering the involved prime bound. For our curves a number of novelties occur. We prove a "higher order" Chabauty theorem to deal with these cases. Finally, to study the isolated quartic points on X0(65), we rigorously compute the full rational Mordell--Weil group of its Jacobian.

M3 - Working paper

BT - Cubic and quartic points on modular curves using generalised symmetric Chabauty

PB - arXiv

ER -