Regulators of Elliptic Curves

TY - JOUR

T1 - Regulators of Elliptic Curves

AU - Autissier, Pascal

AU - Hindry, Marc

AU - Pazuki, Fabien

PY - 2021/4/1

Y1 - 2021/4/1

N2 - We study the regulator of the Mordell–Weil group of elliptic curves over number fields, functions fields of characteristic 0 or function fields of characteristic p>0⁠. We prove a new Northcott property for the regulator of elliptic curves of rank at least 4 defined over a number field. In the function field case, we obtain that non-trivial families of elliptic curves with bounded regulators and bounded ranks are limited families. We conclude by asking new questions.

AB - We study the regulator of the Mordell–Weil group of elliptic curves over number fields, functions fields of characteristic 0 or function fields of characteristic p>0⁠. We prove a new Northcott property for the regulator of elliptic curves of rank at least 4 defined over a number field. In the function field case, we obtain that non-trivial families of elliptic curves with bounded regulators and bounded ranks are limited families. We conclude by asking new questions.

U2 - 10.1093/imrn/rny285

DO - 10.1093/imrn/rny285

M3 - Journal article

SN - 1073-7928

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

ER -